President Trump had touted the raids — called Operation Border Resolve — as a show of force amid an influx of Central American parents and children across the southern border. After postponing the raids in June, Mr. Trump said ahead of time that they would take place last week.

Two current Department of Homeland Security officials and one former department official also confirmed to The Times that an enforcement operation would take place around mid-July.

But the publicity may have prompted many of those who had been targeted — 2,105 people in more than a dozen cities who had received final deportation orders but had not reported to Immigration and Customs Enforcement officers — to temporarily leave their homes, or to move altogether to evade arrest.