Speaker Mike Johnson on Wednesday told Republicans that the House would vote Saturday evening on his foreign aid package for Israel and Ukraine, pushing through resistance in his own party to advance a long-stalled national security spending package for U.S. allies.

His announcement came amid a crush of opposition from Republicans who are vehemently against sending more aid to Ukraine, and have vented for days as congressional aides race to write the legislation Mr. Johnson proposed on Monday.

The legislative package Mr. Johnson is trying to advance roughly mirrors the $95 billion aid bill the Senate passed two months ago with aid to Ukraine, Israel, Taiwan and other American allies, but broken into three pieces that would be voted on individually.

There would be a fourth vote on a separate measure containing other policies popular among Republicans, including conditioning Ukraine aid as a loan, a measure that could lead to a nationwide TikTok ban and fresh sanctions on Iran. It would also pave the way to selling off Russian sovereign assets that have been frozen, in order to help fund the Ukrainian war effort.

The legislation includes $60 billion for Kyiv; $26 billion for Israel and humanitarian aid for civilians in conflict zones, including Gaza; and $8 billion for the Indo-Pacific.

“We’ve taken the Senate supplemental bill and we’ve improved the process and policy, and that’s a really important thing,” Mr. Johnson said on Fox News on Wednesday. “Every member gets to vote their own conscience.”

In a separate interview minutes later on CNN, he added: “We’re not the world’s policeman, but we’re going to do the right thing. And I think the Congress is going to take an important stand.”

After Mr. Johnson released the text of the aid plan on Wednesday afternoon, President Biden endorsed it in a statement and urged its swift passage.

“I strongly support this package to get critical support to Israel and Ukraine, provide desperately needed humanitarian aid to Palestinians in Gaza, and bolster security and stability in the Indo-Pacific,” Mr. Biden said. “I will sign this into law immediately to send a message to the world: We stand with our friends, and we won’t let Iran or Russia succeed.”

The multipart plan has been painstakingly structured to cobble together just enough support from Democrats and mainstream Republicans to pass, over the opposition of the hard right to funding for Ukraine and left-wing Democrats who do not support unfettered aid for Israel. If all four pieces passed the House, they would then be folded into a single bill for the Senate to take up, in an effort to ensure that senators could not cherry-pick pieces to approve or reject.

Its success will require everything to go right for Mr. Johnson this week to prevail.

Mr. Johnson has already faced a tough road since announcing his intent on Monday evening to advance the aid package, over the vociferous objections of conservatives in his conference. On Tuesday, a G.O.P. lawmaker announced that he would join the bid to oust Mr. Johnson spearheaded last month by Representative Marjorie Taylor Greene, Republican of Georgia.

The speaker has met with a parade of Republicans who have tried to convince him to abandon his plan in favor of more partisan proposals, such as abandoning aid for Ukraine entirely. To ensure enough lawmakers attend the votes on Saturday evening to allow for the legislative package’s passage, he has had to manage the schedules of lawmakers eager to leave Washington this weekend to attend fund-raisers and preplanned delegation trips abroad.

Mr. Johnson will also almost certainly need to rely on Democrats to provide the votes necessary to clear the way for it to come to the floor, in an unusual breaking of custom, and for the Ukraine aid itself. A number of Republicans have said they will vote to block the package from coming to the floor in protest.

“Every true conservative America First patriot in the House should vote against the rule for this borrowed foreign aid bill with no border security!” Representative Bob Good of Virginia, the chairman of the Freedom Caucus, wrote on social media.

Another spasm of resistance came later on Wednesday night, when three conservatives on the House Rules Committee signaled that they intended to block Mr. Johnson from bringing a border security bill to the floor for a vote on Saturday, as part of a larger protest over his handling of the legislative package.

Mr. Johnson had announced earlier that he would hold a separate vote on a border security bill “that includes the core components” of House Republicans’ stringent legislation, passed last May, that would crack down on unlawful immigration and revive severe Trump-era border restrictions. That was a nod to ultraconservatives who have demanded that the speaker not advance aid to Ukraine without securing sweeping concessions from Democrats on immigration policy.

But hard-liners on the panel said that the planned vote was just for show — because it would not be bundled with the foreign aid package, and the Senate would not be forced to take it up.

“This is not the way we should be doing business,” said Representative Chip Roy, Republican of Texas. “I believe this is part of a larger effort to push something through for very politically expedient purposes that I’m on record as disagreeing with.”