Both measures have vocal opponents in Congress, however, and their hopes of passage have hinged on a fragile bipartisan coalition to overcome daunting procedural and legislative obstacles.

Speaker of the House Mike Johnson has said he is determined to bring the matter to a vote, even if it may put his hold on power in jeopardy.

The Ukraine vote will be closely watched in Kyiv, which has warned of an urgent need for fresh support from its allies as Russia makes steady gains on the battlefield.

The House is set to vote on final passage on Saturday, and the Senate may approve the package as soon as this weekend. President Joe Biden has pledged to sign it into law.

What's in the aid bills?
Mr Johnson's foreign aid proposal provides $60.8bn (£49bn) to Ukraine, $26.4bn to Israel and $8.1bn to the Indo-Pacific region, including Taiwan. The House of Representatives will vote on each component individually, raising the possibility that some components will be approved and others will fail.

The Speaker is also bringing a fourth piece of legislation to a vote, which includes requiring that Chinese company ByteDance divest itself of the TikTok social media app, authorising the sale of frozen Russian assets, and imposing new sanctions on Russia, Iran and China.

Whatever passes will be combined into one bill that will then have to be approved as a whole by the Senate before it reaches the president's desk.

Mr Johnson has also promised to introduce an immigration reform bill that contains provisions favoured by conservative Republicans in an attempt to win over their support for the aid package.

But the border bill looks unlikely to pass as it would require the support of two-thirds of the House, reports the Washington Post.

Why have they been held up?
Opinion polls suggest that a growing number of Republicans oppose any new aid to Ukraine. Some liberals are against military support for Israel. While these sentiments were not enough to prevent the US Senate from passing legislation that contained support for both nations in February, it has been a different story in the House.

Mr Johnson has a slim majority in the chamber, and a handful of conservatives have threatened to push for his removal if he backs new Ukraine aid. The effort, led by Georgia congresswoman Marjorie Taylor Greene, has two other supporters so far: Thomas Massie of Kentucky and Paul Gosar of Arizona.

Up until now, the Speaker has been reluctant to challenge his right-wing critics. On Wednesday, however, he reversed course, saying his goal was to "do the right thing and let the chips fall where they may".

Meanwhile, left-wing Democrats who object to Israel's conduct of the war in Gaza have said that they will not allow the US to continue to be complicit in a human-rights catastrophe. The Israel aid bill contains $9bn in humanitarian aid, which may help win over some reluctant Democrats.

By allowing separate votes on Israel and Ukraine aid, Mr Johnson hopes to allow individual legislators to vote against provisions they dislike without sinking the entire effort.

What's at stake?
Biden administration officials have warned that the situation in Ukraine is dire. The nation's military is running short on munitions and morale is low, as the Russian army gains ground.

"There is a very real risk that the Ukrainians could lose on the battlefield by the end of 2024, or at least put [Russian President Vladimir] Putin in a position where he could essentially dictate the terms of a political settlement," CIA Director William Burns said during a speech in Texas on Thursday.

In an interview with the BBC on Wednesday, Ukrainian Prime Minister Denys Shmyhal said his nation needed new support "yesterday, not tomorrow, not today" and warned that Ukraine would fall without American aid.

The situation for Israel's military is vastly different to the situation for Ukraine's military. But Mr Biden said that the nation's high-tech air defences - which received their most formidable test in last weekend's Iranian missile and drone assault - needed to be replenished.

"This is a pivotal moment," Mr Biden wrote in a Wall Street Journal opinion piece on Wednesday that called for the House of Representatives to act.

So will they pass?
Late on Thursday night, Democrats joined with Republicans allied with Mr Johnson to ensure that the aid legislation cleared a formidable procedural hurdle in the House Rules Committee despite dissent in conservative ranks.

On Friday morning, a similar coalition of Democrats and pro-aid Republicans in the full House voted 316-94 to set up debate and final votes on the legislation on Saturday afternoon. This comfortable margin is a strong indication that a large bipartisan majority in the chamber is on course to approve the package.

Democratic support could also give Mr Johnson a political lifeline, as his strategy of bypassing his party's hardcore conservatives to enact legislation may prompt them to follow through on their threats to force a vote on his removal.

A Speaker having to rely on the backing of the minority party, particularly on procedural votes, is rare in modern congressional history. But Mr Johnson's hold on power is tenuous, and the legislators who oppose him and his bid to provide aid to Ukraine occupy some key positions within the House's power structure.

Talking to reporters on Friday, House Democratic leader Hakeem Jeffries of New York said Mr Johnson had had to manage a "very unruly" group of Republicans and praised him for working to bring Ukraine aid to a vote.

Democrats may be wary of offering help to Mr Johnson, but the prospect of providing new aid to Ukraine - a top foreign policy priority to their party and Mr Biden - could make it worth the effort.

And that effort appears to be close to paying off.

By Anthony Zurcher,BBC News, Washington