U.S. Immigration and Customs Enforcement is considering a plan to reduce its detention capacity significantly after Republicans in Congress blocked a bill that would have provided the agency with more than $7 billion, officials said Wednesday.

To stay within its current budget, ICE would need to cut detention levels by more than 10,000 spots within months, according to documents laying out the proposal, which were obtained by The New York Times. The agency could either release some of the 38,000 people in custody now, or decline to fill vacant spots as cases get resolved.

Three officials familiar with the plan said it was under active consideration within ICE. The officials spoke on the condition of anonymity to discuss what they described as contingencies.

The proposal was first reported by The Washington Post.

The plan comes at a moment of crisis over immigration in the United States, with record numbers of people crossing into the country and the asylum system all but broken. Bitter politics have paralyzed any movement on the issue, as Republicans seize on it as a political weapon against President Biden.

Mr. Biden has implored Congress to pass bipartisan legislation that would have clamped down on migration at the southern border. But his predecessor and likely challenger in this year’s election, former President Donald J. Trump, pressured Republicans to block the deal, saying it would be a “gift” to Democrats.

In effect, many Republicans now reject a deal they had previously demanded, blocking the kind of measures, like stricter enforcement by ICE, that they have sought for years.