Speaker Mike Johnson on Tuesday encountered stiff resistance from Republicans as he embarked on a complicated and politically perilous strategy to push legislation through the House to send aid to Israel and Ukraine — all while beating back a threat to his own job.

Mr. Johnson, who has agonized for months over whether and how to advance aid to Ukraine that many in his party bitterly oppose, has settled on a multipart plan that will require everything to go right for him this week to prevail.

It aims to bring together a complicated mix of bipartisan coalitions and allow different factions in the House to register their opposition to pieces of the aid package without sinking the entire thing. And it would ultimately mean cobbling together just enough support from Democrats and mainstream Republicans to pass the legislation amid resistance from hard-right Republicans to Ukraine funding and among left-wing Democrats to unfettered aid for Israel.

Mr. Johnson plans to advance a legislative package that 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 down into three separate pieces that would each be voted on individually. There would also be a fourth vote on a separate measure containing other policies popular among Republicans, including conditioning Ukraine aid as a loan.

The strategy has run into a flurry of opposition from members of his own party, including one Republican, Representative Thomas Massie of Kentucky, who on Tuesday announced that he would join a threatened bid to remove Mr. Johnson from the top post.