Gov. Kathy Hochul of New York on Monday proposed an expansion of the state’s child tax credit that would more than double what some families currently receive.

The plan, the second in a series of recent proposals the governor has made toward addressing the state’s affordability crisis, would give eligible families a tax credit of up to $1,000 per child under the age of 4. Each child from the age of 4 to 16 will qualify families to receive up to a $500 tax break per child.

In recent years, the state has offered up to $330 per child for the poorest New York families. Ms. Hochul will include the proposal in her State of the State address next week and push to include it in her executive budget.

Frustration with the high cost of living surfaced among voters in the 2024 elections, and many Democrats, amid soul searching about Republican victories, said they should have talked more about addressing affordability.

Both Ms. Hochul and Mayor Eric Adams of New York City have already announced tax cuts or refunds they want the Legislature to adopt this year. Mr. Adams’s proposal would eliminate New York City income taxes for more than 400,000 of the lowest-wage earners. Ms. Hochul announced in December that she wants to spend about $3 billion to send checks between $300 and $500 to roughly 8.6 million New Yorkers, using money from sales tax revenue.

In a news conference Monday, Ms. Hochul said she has long focused on affordability, adding that proposals like increasing the child tax credit are partly shaped by raising her own children and seeing the financial strain that experience can have on a household.

“I will continue doing this,” she said. “I’ll do it independent of elections. It’s the right thing to do.”

“People are hurting right now,” she added, “and we cannot be tone deaf as a party, as a nation or as a state to those cries for help. This is how to respond to them.”

The state has spent billions in recent years on child care and to make more families eligible for subsidies. Tax credits like the one Ms. Hochul proposed have proved popular and effective. During the early years of the coronavirus pandemic, an expansion of the federal child tax credit led to dramatic reductions in adolescent poverty. This expansion then expired, and bipartisan efforts to bring it back failed.

Ms. Hochul’s proposal would apply to more than 2.75 million children in the state; families earning up to $200,000 a year would be eligible for the credit. In a news release, Ms. Hochul’s team said the average credit for families would double to nearly $950 under her proposal.

Legislative leaders, who have suggested similar proposals in past budget negotiations, appeared receptive.

“We are very glad the governor is supporting these important tax credits, which we have long championed in the Assembly majority,” said Mike Whyland, a spokesman for Assembly Speaker Carl E. Heastie.

State Senator Andrea Stewart-Cousins, the majority leader, noted in a statement that she, like Ms. Hochul, is both the first mother and grandmother to serve in her role. Funding child care would remain a focus this legislative session, she said.

“I know firsthand how expensive raising children has become in this great state,” she said. “We look forward to discussing this proposal further. But we also know we have to deal with the rising cost of child care. The cost of child care is a burden that can overwhelm families, and we need to take steps to make affordable child care available to all New Yorkers.”

Even some Albany Republicans were open to the proposal. State Senator Jacob Ashby, a Republican from Rensselaer County, said that the state needs to do more “to make structural changes to our state economy” like lowering taxes across the board. Many of his colleagues have criticized Ms. Hochul, arguing that her administration has not done enough to lower costs for New York families.

“As someone who’s sponsored bipartisan legislation to provide new parents with targeted relief and pushed to increase the child tax credit across the board, I’m really optimistic about this proposal,” Mr. Ashby said in a statement.

If enacted, Ms Hochul’s proposal would be among the most generous child tax credits nationwide, according to researchers at the Center on Poverty and Social Policy at Columbia University. In 2023, New York and 15 other states had some form of this credit, ranging in the amount given to families and the income threshold when it phases out. When the proposal is fully up and running in several years, these Columbia researchers estimate the tax cut could drop child poverty by about 9 percent.

“When the federal child tax credit was expanded during the pandemic, we saw child poverty plummet to historic lows,” said Richard Buery Jr., the chief executive of the Robin Hood Foundation, a nonprofit in New York City that works to reduce poverty.

“With more money in your pocket, as a parent, you are less stressed, you can be more present, you can be much better and more effective at parenting children,” Mr. Buery added. “But when those federal credits expired, we saw our local poverty rate reach a 10-year high. So we know what to do. We just need the political leadership to do it.”