By Joey Roulette and David Morgan

WASHINGTON (Reuters) -Republicans in the U.S. House of Representatives face new pressure to select a speaker after Israel declared war on Sunday, following a rare attack by Hamas militants that has prompted calls for more U.S. military aid.

Some Republicans, including Representative Jim Jordan, a top candidate for the job, also want lawmakers to agree on how to move forward on the thorniest issue the House faces – federal spending for the current year – when they choose a new speaker.

The U.S. in 2016 pledged $3.8 billion in annual aid to Israel under former President Barack Obama, part of a record 10-year $38 billion aid deal that guarantees weapons, ammo and other military support.

House Republicans are expected to hear from speaker candidates behind closed doors on Tuesday and vote to choose their nominee on Wednesday. A House floor vote to elect a replacement for Republican former Speaker Kevin McCarthy could come later in the week.

Until then, the chamber cannot approve new aid.

"It's not ideal," Republican Representative Michael McCaul told CNN on Sunday. "What kind of message are we sending to our adversaries when we can't govern, when we're dysfunctional, when we don't even have a speaker of the House?"

Jordan and others also want a spending agreement, which could avert a government shutdown next month.

"When we walk out of that room … we've got to have 218 votes for a Republican speaker and we've got to have 218 votes for how we deal with Nov. 17, when the funding bill for the government comes due," Jordan, who is battling the House's No.2 Republican Steve Scalise of Louisiana for speakership, told Fox News on Sunday.

Hardliners pushing for cuts that would reduce government funding to fiscal 2022 levels have divided House Republicans for months and brought Congress to the brink of a government shutdown just over a week ago.

Any House bill that includes severe spending cuts is unlikely to pass the Democrat-controlled Senate.

"I am not going to support anybody until the conference figures out spending," Republican Representative Ken Buck told ABC's "This Week" on Sunday.

Securing the 218 votes to elect a new speaker behind closed doors would avoid a recurrence of the 15 floor votes that preceded McCarthy's election to the speakership in January.

Matt Gaetz, the Florida congressman who led McCarthy’s ouster, downplayed the speaker election's impact on Israel's security needs, suggesting on NBC’s "Meet the Press" that the U.S. could fulfill the country's requests.

U.S. President Joe Biden told Israeli Prime Minister Benjamin Netanyahu on Sunday that "additional assistance for the Israeli Defense Forces is now on its way to Israel," and that more would follow in the coming days, the White House said.

"The actions taken by some members of my party were wholly irresponsible without this going on," Republican presidential candidate Chris Christie told ABC's "This Week". "They're now even putting a brighter light on the irresponsibility of not having someone in place."

(Reporting by Joey Roulette and David Morgan; Editing by Heather Timmons and Lisa Shumaker)