WASHINGTON — President Trump on Saturday delayed plans for nationwide raids to deport undocumented families, but he threatened to unleash Immigration and Customs Enforcement agents in two weeks if Democrats do not submit to changes in asylum law they have long opposed.

The announcement, made on Twitter as Mr. Trump was meeting with aides at Camp David, was the president’s latest attempt to pressure his adversaries into making immigration changes. Last month, he threatened to levy tariffs on Mexico unless it did more to stop the flow of migrants into the United States.

Immigration agents had been planning to sweep into several immigrant communities in 10 major cities — including Miami, Los Angeles, Baltimore and Chicago — beginning on Sunday. Officials said on Friday that they had targeted about 2,000 families in a show of force intended to demonstrate their strict enforcement of immigration laws. Children of immigrants — some of whom were born in the United States — had faced the prospect of being forcibly separated from their undocumented parents.

Mark Morgan, the acting director of Immigration and Customs Enforcement, had announced this month that his agency would begin the raids at some point in the future. But on Monday, Mr. Trump revealed on Twitter that they would start the following week, claiming that officials would deport millions of people and sending panic through cities across the country.