WASHINGTON — House Republicans on Thursday presented a plan for a stopgap bill that would fund the Department of Homeland Security for three weeks, raising hopes of averting a looming shutdown of the agency.

The plan, which the leaders pitched to rank-and-file Republicans in a closed-door meeting, was the first sign they were willing to pass a new bill after passing another one weeks ago that takes aim at President Obama’s executive actions on immigration and has been blocked in the Senate.

Facing a Friday night-into-Saturday morning shutdown deadline, the plan could ultimately win support from lawmakers in both parties on Friday. But its passage would only continue a standoff over longer-term DHS funding between the House and the Senate. Separately, the Senate was moving toward a final vote on a funding bill that would not go after Obama’s immigration directives.

Exiting the House GOP meeting, Republican members said the leadership presented a plan as a way to allow time for the House and Senate to try to go to conference on their competing bills. But Senate Democratic leaders have rejected the idea of a conference.

Rep. Walter Jones, R-N.C., a foe of House Speaker John Boehner, R-Ohio, said he would not support the plan but that “of those that spoke,” a “majority, probably, are inclined to support it.”The Republicans’ meeting came as the Senate’s bill appeared unlikely to face tactical delays from rogue conservative senators who want to battle Obama. The measure could win final passage as soon as Friday.

One of the leading critics of the president’s immigration actions, Sen. Jeff Sessions, R-Ala., said that he did not plan to hold up the measure and was “not aware” of others planning to do so.

But House Republican leaders, bent on fighting Obama’s directives, did not embrace the Senate plan.

Boehner declined to say whether he would take the Senate bill up in his chamber. “We’ll wait to see what the Senate can or can’t do,” Boehner told reporters. He accused Senate Democrats of “blackmail to protect the actions of the president.”

Meanwhile, Democrats ramped up pressure on the Boehner to simply take up the Senate bill. Speaking at a joint news conference, Senate Minority Leader Harry Reid, D-Nev., and House Minority Leader Nancy Pelosi, D-Calif., called on Boehner to swiftly bring it to a vote and warned him not to amend it with immigration riders.

Reid declined to say whether he would try to block a short-term stopgap bill if the House passed one. Pelosi argued that a short-term bill is not an ideal solution.