President Trump’s next round of punishing tariffs on some of America’s largest trading partners was set to go into effect just after midnight on Wednesday, including stiff new levies that will increase import taxes on Chinese goods by at least 104 percent.

Mr. Trump acknowledged on Tuesday that his tariffs had been “somewhat explosive.” But throughout the day he continued to defend his approach, saying that it was encouraging countries with what he calls “unfair” trade practices to offer concessions.

“We have a lot of countries coming in to make deals,” he said during remarks at the White House on Tuesday afternoon. At a dinner with Congressional Republicans in Washington later that evening, he said other countries wanted to make a deal with the United States but he was happy just collecting the revenue from tariffs, which he claimed would reach $2 billion a day.

“I know what the hell I’m doing,” he said, adding that he would announce “a major tariff on pharmaceuticals” very shortly.

The president and top administration officials signaled on Tuesday that the White House was ready to negotiate deals, saying that 70 governments had approached the United States to try to roll the levies back. Mr. Trump said officials would begin talks with Japan, South Korea and other nations.

The president, whose punitive and successive tariffs on China have triggered a potentially economically damaging trade war, also said he was open to talking to Beijing about a deal.

“China also wants to make a deal, badly, but they don’t know how to get it started,” Mr. Trump wrote on social media. “We are waiting for their call. It will happen!”

On April 2, the president imposed a 10 percent global tariff on hundreds of countries and promised far steeper “reciprocal” tariffs on April 9 for nations that he maintains have “ripped off” America. Much of his anger has been directed at China, which exports far more into the United States than it buys. Since February, the president has imposed successive rounds of tariffs on China. On Wednesday, the minimum tax on Chinese imports will hit 104 percent. Some products may face even higher levies if they are subject to tariffs that Mr. Trump imposed during his first term.

The president’s approach has prompted retaliation from China and caused other countries to draw up their own plans to hit American exports. As a result, economists have raised their expectations for a recession in the United States, and many now consider the odds to be a coin flip.

Mr. Trump has dismissed those concerns and said he will not back away from his trade agenda. The president says his approach is necessary to return manufacturing and industrial production to the United States. He and his economic advisers have pointed to recent offers by countries to lower their own tariffs, though some officials have given mixed signals about how willing the president will be to negotiate.

News that the administration was considering reaching agreements with trading partners helped to buoy stock markets after three days of punishing losses. But by Tuesday afternoon the S&P 500 had given up any gains and closed down for the fourth consecutive trading day.

Karoline Leavitt, the White House press secretary, said in a briefing on Tuesday afternoon that Mr. Trump had spoken with the prime minister of Japan on Monday and that the United States would be seeking deals. She said that the president had asked his advisers to “have tailor-made trade deals with each and every country that calls up this administration to strike a deal.”

But Ms. Leavitt rejected the idea that the request represented an “evolution” from aides’ earlier comments that there would not be a negotiation over tariffs. She said the president was not planning to pause his plan. “He expects these tariffs are going to go into effect,” she said.

Ms. Leavitt also insisted that the United States had the upper hand when it came to negotiations. “America does not need other countries as much as other countries need us, and President Trump knows this,” she said.

Mr. Trump’s Treasury secretary, Scott Bessent, made similar comments on Tuesday as he assailed China for retaliating against the United States with tariffs of its own and warned that America had more leverage in a trade war with the world’s second-largest economy.

“What do we lose by the Chinese raising tariffs on us?” Mr. Bessent said on CNBC. “We export one-fifth to them of what they export to us, so that is a losing hand for them.”

Jamieson Greer, Mr. Trump’s top trade official, defended the administration’s aggressive tariff moves before a Senate committee on Tuesday morning, arguing that the U.S. economy was facing “a moment of drastic, overdue change” after decades of factories moving overseas and hurting the American working class.

Mr. Greer said that the president had imposed the tariffs to achieve “reciprocal treatment from other countries.” He added that the policy was already working, citing announcements that companies have made in recent weeks of investments in the United States.

He declined to say how long the tariffs would be in effect, saying that the administration was looking at it “country by country.” But he implied that there might not be quick remedies.

“Our large and persistent trade deficit has been over 30 years in the making, and it will not be resolved overnight, but all of this is in the right direction,” Mr. Greer said.

Mr. Bessent, who will oversee negotiations with Japan along with Mr. Greer, also indicated an openness to negotiating deals.

“I think you are going to see some very large countries with large trade deficits come forward very quickly,” Mr. Bessent said. “If they come to the table with solid proposals, I think we can end up with some good deals.”

Other officials have been less optimistic about the possibility of countries finding a way to avoid the tariffs.

“This is not a negotiation,” Peter Navarro, a White House trade adviser who is a strong supporter of tariffs, wrote in an opinion essay on Monday. “For the U.S., it is a national emergency triggered by trade deficits caused by a rigged system.”

Mr. Trump’s aggressive tariffs have prompted sharp blowback from Democrats in Congress and increasing nervousness from Republicans, who are under pressure from constituents to defend their export markets.

A bipartisan group of senators — including Ron Wyden of Oregon, the top Democrat on the committee; the minority leader, Chuck Schumer of New York; and one Republican, Rand Paul of Kentucky — plans to introduce a resolution later this week that would terminate the national emergency the president declared to introduce his tariffs.

But the measure would face a tough path to passage. If the House approves it, Congress will need enough votes to override the president’s veto. And the House may take action so it is not forced to vote on the resolution.

Last week, the Senate approved a similar measure to scrap the tariffs that Mr. Trump imposed on Canada, but House Republicans moved pre-emptively to shut down the requirement that they vote on such a measure.

Representatives Don Bacon of Nebraska and Jeff Hurd of Colorado, both Republicans, introduced a bipartisan House bill on Monday that would give Congress the final say on any proposed tariffs. The measure, cosponsored by two Democrats, Representatives Josh Gottheimer of New Jersey and Gregory W. Meeks of New York, has not yet drawn any other Republican supporters.

But Mr. Bacon said on Monday that he had spoken to several other colleagues — “like, 10 to 20” — who said they liked the proposal but wanted to wait and hear from Mr. Greer on Capitol Hill. On Wednesday, Mr. Greer will testify before the House Ways and Means Committee.

Several Senate Republicans had forceful exchanges with Mr. Greer on Tuesday about whether the tariffs were a negotiating tool and whether businesses that depend on imported products might find relief.

“We need to think strategically about tariff policy, including how to minimize unnecessary costs on American families,” Senator Michael D. Crapo, the Republican chairman of the finance committee, said. “I also recognize that although it is easy to see the costs arising from tariffs, it is far more difficult to assess the cost of denied market access opportunities.”

Senator Steve Daines, a Republican from Montana, said he was concerned about the inflationary effect of tariffs on consumers. But he said he was encouraged that other countries were approaching the United States to negotiate. He said that stock markets were rebounding Tuesday because “there’s hope that these tariffs are means and not solely an end,” he said.

Senator Charles E. Grassley of Iowa, one of the few Republicans who have signed on to legislation opposing Mr. Trump’s tariffs, said that agriculture “is usually the first place of retaliation.”

During the trade fight with China in Mr. Trump’s first term, U.S. agricultural exports plummeted after China imposed high retaliatory duties on soybean, corn, wheat and other American imports, and the United States spent about $23 billion to support American farmers.

Mr. Grassley said that he supported the president generally but believed that Congress had delegated too much authority to him over trade. He said he had taken a “wait and see” approach to tariffs because he believed Mr. Trump and Mr. Greer were using them as a tool to get fairer trade.

“If that’s not the case, level with me,” Mr. Grassley told Mr. Greer.

The Retail Industry Leaders Association, which represents major companies like Walmart, Target, Starbucks and Best Buy, released a statement ahead of Mr. Greer’s testimony saying that the tariffs had caused “disruption and uncertainty in the markets and with consumers” and could drive up prices for products like baby clothes, handbags and paper plates.

“Americans elected President Trump to lower inflation and grow the economy,” the group said. “Instead, these broad-based tariffs threaten family pocketbooks and risk destabilizing confidence in the economy.”

For Democrats, the tariffs have provided plenty of fodder to argue that Mr. Trump is mismanaging the economy.

“The U.S. economy has gone from the envy of the world to a laughingstock, in less time than it took to finish March Madness,” Mr. Wyden said on Tuesday. “Through it all, Donald Trump and his advisers have yet to provide any understandable explanation at all for what his tax hike on the American people is supposed to accomplish.”

“Donald Trump is single-handedly driving this economy off a cliff with no evidence to back him up,” said Senator Elizabeth Warren, Democrat of Massachusetts.

Maya C. Miller, Tony Romm and Tyler Pager contributed reporting.