Congressman Mike McCaul, the chairman of the House Foreign Affairs committee, urged his party to unify as "we have got to move quickly, we cannot paralyse democracy, especially when we have hotspots all over the world," likely a reference to the erupting violence in Israel and the West Bank.
"I'm just worried about the messaging this sends," he said, during an interview with CNN.
Last week eight hard-right Republicans, led by Congressman Matt Gaetz, managed to oust Mr McCarthy from the Speakership. The move was largely seen as a punishment for his decision to work with Democrats to avert a government shutdown.
Mr McCaul told CNN's State of the Union that it was imperative that the House choose a speaker to ensure legislation makes it back to the floor.
Such legislation could include a bipartisan condemnation of Hamas following its attack on Israel, as well as action helping in Israel's defence and siege of the West Bank.
“It’s too dangerous a time right now to be playing games with national security,” he said.
Mr McCaul expressed concerns that Israel's response could escalate the violence in the region at a time when the House is in disarray.
“If this lights up into a larger jihadist war against the zionist, if you will, that’s always what keeps everyone up at night,” he said.
Speaking to NBC’s Meet the Press, Mr Gaetz insisted that the shakeup in the House would not hinder the US’s ability to assist Israel, saying there was “no need in Israel that we’re not going to be able to meet based on the funding that we’ve already approved for Israel.”
He went on to express some confidence that the House Republicans were ready to "unify around one speaker and not have this civil war."
Congressmen Jim Jordan and Steve Scalise have both voiced their intention to run for House speaker, while Congresswoman Marjorie Taylor Greene has insisted that Donald Trump — who has backed Mr Jordan for the spot — should take the spot.
Despite his optimism, Mr McCaul noted during the interview that he was not a supporter of the move to oust Mr McCarthy.
“It was not my idea to oust the speaker, I thought it was dangerous…[considering] all the threats that are out there,” he told CNN.
He said the move sent the message to America's "adversaries" that the House "cannot govern" and is "dysfunctional."
"I mean how does Chairman Xi of China look at that when he says democracy doesn’t work, how does the Ayatollah look at this, knowing that we cannot function properly?” he asked.
In a rare show of bipartisan agreement, House minority leader Hakeem Jeffries shared similar sentiments to CNN's State of the Union, saying it was "time for the GOP to end the Republican civil war," citing the need to get back to normal legislative sessions.
In the meantime, House Republicans are mulling over whether or not to nix the "motion to vacate" rule allowing one individual to move to remove a Speaker. Over a fifth of the House Republicans signed an open letter calling for a change to the rule.
“It is our responsibility to identify the right person at this moment to lead us into the future to achieve the conservative policy objectives that we and the American people all share,” the members wrote. “We cannot allow our majority to be dictated to by the alliance between the chaos caucus and the minority party that will do nothing more than guarantee the failure of our next Speaker.”
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