WASHINGTON — House Republicans moved Thursday to create a bill that would fund most of the Department of Homeland Security while preventing President Obama from carrying out his recent executive action on immigration, in an effort to appease their more conservative members.

If that approach passes the House, however, it is unlikely to clear the Senate, where Republicans will need at least half a dozen Democratic votes to overcome a filibuster. And even if the Senate approves the measure, Mr. Obama has threatened to veto Republican legislation that would undo his immigration action. Funding for the department is set to run out at the end of February, something both parties hope to avoid.

Many conservatives see the funding bill as their best leverage to undo Mr. Obama’s immigration plan, which will allow as many as five million undocumented immigrants to live and work in the country.

“The House will soon take action aimed at stopping the president’s unilateral action when it comes to immigration,” Speaker John A. Boehner of Ohio said. “I said we’d fight it tooth and nail when we had new majorities in the House and Senate, and I meant it.”