Lawyers for the American Civil Liberties Union on Tuesday renewed their efforts to prevent the Trump Administration from deporting Venezuelan migrants under a wartime powers act, asking a Manhattan judge to again block the White House from using the law.

The filing followed a Supreme Court decision on Monday that had allowed the government to resume deportations, an early ruling on an issue that has set up a major clash between President Trump and the federal judiciary.

The Supreme Court addressed few of the case’s substantive issues. Instead, it ruled on narrow procedural grounds: The justices said that, because the migrants were confined in Texas, the A.C.L.U.’s case should have been filed there, rather than in Washington.

But on Tuesday, the A.C.L.U. filed a similar petition in a New York federal court, noting that two migrants who were subject to deportation were being held in a jail in Goshen.

The administration’s efforts to deport Venezuelan migrants have set off one of the most contentious legal battles of President Trump’s second term. It began last month, after the president invoked the Alien Enemies Act, a seldom-used wartime statute from 1798, seeking to authorize the deportation of people he claimed were members of Tren de Aragua, a Venezuelan criminal gang.

A.C.L.U. lawyers representing the targeted migrants immediately challenged the order in Washington federal court, even as the administration sent at least 137 migrants to a prison in El Salvador. The lawyers have said the government misconstrued the Alien Enemies Act, and that the law was intended to be used only during an “invasion” or “predatory incursion” by a foreign nation or government.

The judge hearing the case, James E. Boasberg, expressed skepticism about the government’s use of the statute. He said he was concerned that the migrants had no way to contest whether they were gang members and prohibited the administration from continuing to use it as justification for deportations. It was his order that the Supreme Court overturned on Monday.

The A.C.L.U.’s petition on Tuesday sought a similar order from a New York judge, Alvin K. Hellerstein. It sought to prohibit the deportation of the two unnamed men being held in Goshen — and all others in similar situations.

The first of the men is a 21-year-old who fled Venezuela after having been threatened by members of the Tren de Aragua gang because of his sexual orientation, the A.C.L.U. said in its filing. The second is a 32-year-old who applied for asylum after having protested the actions of the Venezuelan president, Nicolas Maduro, and later fled the country, fearing that he would be imprisoned, tortured and killed for his activism.

The administration has argued that it is justified in using the Alien Enemies Act, saying that Tren de Aragua members are “dangerous aliens who pose threats to the American people.”

Critics of the government have raised concerns about the misidentification of some of the migrants, who were quickly moved out of the country without being given a chance to challenge their detention.

The Supreme Court did not rule on that issue. But it did say that the government needed to inform migrants within a reasonable amount of time that they were subject to deportation, allowing them to seek relief in the proper court.

Jurisdictional issues — the question of which court should hear a case and why — have dominated the early proceedings in several high-profile immigration cases.

In addition to the Venezuelan migrant case, the case of Mahmoud Khalil, a Columbia University graduate student and a leading figure in pro-Palestinian protests, has mostly been dominated by questions of where the case should be heard. While Mr. Khalil is being held in Louisiana, the case for his release is playing out in New Jersey.