And it would increase funds for the federal Secure Communities program. Under that program, fingerprints of every individual booked by the police were checked against Homeland Security databases, leading immigration authorities to initiate many deportations. The program faced growing resistance from immigrant advocates and states and was canceled by the president.

During the appropriations process at the end of last year, House Republicans insisted on offering only short-term funding for homeland security, to give themselves leverage to revisit the issue this year, when they control both chambers and believe they are in a better position to fight the president on his immigration directives.

“The American people were expecting the leadership to step up to the plate and not just make some kind of symbolic gesture in trying to address what the president did back in November, but try to go a step further,” said Representative Robert B. Aderholt, Republican of Alabama and a member of the House Appropriations Committee. “That’s what our language does, and what at the end of the day will garner a lot of support from our colleagues.”

The House expects to vote on the bill next Tuesday or Wednesday, before congressional Republicans head out of town for a retreat in Hershey, Pa.

However, the Senate is unlikely to pass the House’s initial legislative offering, and Mr. Obama is all but certain to veto it — setting up a showdown that could hold up financing for the entire department. Republicans on Friday were clear that they did not want to risk a shutdown of homeland security, forcing them to straddle a risky balance between funding most of the department while also stripping out money for the president’s unilateral immigration actions.

“We have to D.H.S. funded, it’s as simple as that,” said Peter T. King, Republican of New York.

Democrats and immigration activists were outraged, vowing to fight the Republican proposal.