House Republicans on Wednesday accused the Democratic mayors of New York, Denver, Boston and Chicago of harboring criminal immigrants in an acrimonious congressional hearing over what role large cities should have in the Trump administration’s immigration crackdown.

Under fiery and angry questioning from Republicans on the House Oversight Committee, the mayors defended their policies and their cities’ efforts to house and feed migrants, tens of thousands of whom were bused to their communities by Republican governors. The mayors rejected the notion that the local police should help in the administration’s deportation efforts.

“We do not have the capacity for our law enforcement to be doing federal immigration enforcement,” Mayor Mike Johnston of Denver told lawmakers. “But we want to be partners in making sure we are pulling violent criminals off the street.”

Mr. Johnston spoke of the influx of 42,000 migrants two years ago, many bused from Texas, “mostly women and children in 10-degree weather with only sandals and a T-shirt.”

The hearings seemed to capture the political moment. It was a clash of the law-and-order Republican Party led by President Trump and liberal politicians running cities, broadly known as sanctuary cities, that have large populations of immigrants.

Even the language employed by both sides underlined the stark differences in the ways the two parties approach the issue. The chairman of the committee spoke of “illegal aliens,” a term now out of favor among Democratic leaders and immigrant advocates, who prefer the term “undocumented.”