President Trump continues to push the offer of amnesty to 1.8 million Dreamers. Early Monday, the president sent out a tweet encouraging the Democrats to cut a deal on DACA. The constant push is rubbing many of his supporters the wrong way, including I.C.E.

I.C.E. says the agency opposed Trump’s immigration framework, concluding that the proposed amnesty would leave “gaping holes” for a new wave of illegal immigration.

National I.C.E. Council President Chris Crane sent a letter to Mr. Trump on Friday saying the four-point plan the White House proposed coupling legalization for illegal immigrant Dreamers with a border wall and changes to legal immigration falls short, leaving businesses free to continue hiring illegal immigrants and refusing to root out cities and counties serving as sanctuaries.

“We simply cannot in good faith support any legislative effort on immigration that does not include provisions regarding immigration detainers, sanctuary cities and the smuggling and trafficking of children across U.S. borders,” wrote Mr. Crane, whose organization represents 7,500 employees at U.S. Immigration and Customs Enforcement, the agency that handles deportations and interior enforcement.

“I’ve been saying this for months, and I am thrilled to see the Border Patrol and now ICE are disappointed in the president’s upside down plan for immigration. He has departed from his campaign principles, and people are growing concerned,” said Dennis Michael Lynch, the CEO of DML News.

The letter marks a significant break for the ICE Council, which endorsed Mr. Trump in 2016 — backing that, along with support from the National Border Patrol Council, he trumpeted in campaign speeches.

Mr. Crane’s letter does not withdraw support from the president but says the path he is taking in immigration negotiations undercuts the security promises Mr. Trump made.