Speaker Mike Johnson pledged Saturday that the House would hold a vote next week on legislation to speed $17.6 billion in security assistance to Israel with no strings attached, a move likely to complicate Senate leaders’ efforts to rally support for a broader package with border security measures and aid to Ukraine.

Mr. Johnson’s announcement to members of his conference came as senators were scrambling to finalize and vote on a bipartisan national security bill that has taken months to negotiate. The move could further erode G.O.P. support for the emerging compromise, which was already flagging under criticism from party leaders like Mr. Johnson and former President Donald J. Trump.

Mr. Johnson, a Louisiana Republican, has said that the Senate package would be dead on arrival in the House, arguing that its border security measures are not stringent enough to clamp down on a recent surge of immigration. He said the House would instead focus its efforts on the impeachment of Alejandro N. Mayorkas, the homeland security secretary — a vote on which is now expected to take place next week.

In a letter to his members Saturday, he said the House would also prioritize its own approach to helping Israel’s war effort against Hamas, regardless of what — if any — related legislation the Senate might produce.

“Their leadership is aware that by failing to include the House in their negotiations, they have eliminated the ability for swift consideration of any legislation,” Mr. Johnson wrote, adding that “the House will have to work its will on these issues and our priorities will need to be addressed.”

Senate negotiators have been working on a sweeping national security funding bill to address Republican demands that any legislation sending military aid to Ukraine also significantly improve security at the southern border with Mexico. The emerging legislation, which includes measures making it more difficult to claim asylum and increasing both detentions and deportations, would also send more military aid to Ukraine and Israel, dedicate humanitarian assistance to Palestinians in Gaza and fund efforts to counter Chinese threats to the Indo-Pacific region.

Senator Chuck Schumer, Democrat of New York and the majority leader, announced this week that the Senate would vote no later than Wednesday on whether to take up the bill, the text of which negotiators are expected to publicize no later than Sunday.

But the measure is already facing stiff headwinds from Senate Republicans who think the border enforcement provisions ought to be tougher, as well as those loath to take a politically challenging vote for a bill that is all but assured to die at the G.O.P.-led House’s door.

Several Republicans in the Senate and the House have clamored for a split approach that would address Israel’s war effort separately from Ukraine and the border. Late last year, the Democratic-led Senate rejected a G.O.P. attempt to force a vote on an earlier Israel aid bill that was backed by the House. Democrats objected to the way that the House G.O.P. bill sought to pay for the funds, by making cuts to the Internal Revenue Service.

In his letter Saturday, Mr. Johnson acknowledged that history.

“Democrats made clear that their primary objection to the original House bill was with its offsets,” he wrote, adding that with the new Israel package, “the Senate will no longer have excuses, however misguided, against swift passage of this critical support for our ally.”

The new bill, which was unveiled by House appropriators, is larger than the House’s previous Israel measure, which totaled $14.3 billion. President Biden had sought that amount for Israel as part of a larger request he made in October for supplemental funds to address various global crises, including Ukraine.

The $17.6 billion House measure would direct $4 billion to replenishing Israel’s missile defense systems known as Iron Dome and David’s Sling, as well as $1.2 billion to counter short-range rocket and mortar attacks. An additional $8.9 billion would go toward supplying Israel with weapons, helping it produce its own and replenishing defense stock the United States has already provided; while $3.5 billion would go toward supporting U.S. military operations, embassy security and efforts to evacuate American citizens in the region.