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President Trump received fierce pushback -- including some from fellow Republicans -- on Tuesday night after firing Chris Krebs, the director of the Cybersecurity and Infrastructure Security Agency (CISA), following efforts by Krebs to rebut the president's claims of widespread voter fraud.

But Krebs is also taking some criticism, with one senior DHS official telling Fox News he was “out of his lane” regarding election fraud allegations.

The Tuesday evening firing happened after Krebs led a campaign at CISA to control rumors about election fraud. Trump, in a pair of tweets, said that Krebs had made a statement on election security that "was highly inaccurate, in that there were massive improprieties and fraud -- including dead people voting" and more.

Trump added: "Therefore, effective immediately, Chris Krebs has been terminated as Director of the Cybersecurity and Infrastructure Security Agency."

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"Honored to serve. We did it right. Defend Today, Secure Tomrorow (sic)," Krebs responded in a tweet.

Krebs also linked to the CISA rumor control webpage, and made a "Star Wars" joke in response to a tweet from Luke Skywalker actor Mark Hamill.

"In defending democracy, do or do not, there is no try," Krebs said. "This is the way."

But pushback also came from others, including President-elect Joe Biden, who Trump has so far refused to concede the election to, citing numerous pending legal challenges and recounts. 

"Chris Krebs should be commended for his service in protecting our elections, not fired for telling the truth," Mike Gwin, a Biden spokesperson, said.

"Bipartisan election officials in the administration itself -- and around the country -- have made clear that Donald Trump’s claims of widespread voter fraud are categorically false and Trump’s embarrassing refusal to accept that reality lays bare how baseless and desperate his flailing is," Gwin added. 

House Majority Leader Steny Hoyer, D-Md., also criticized the president for the firing, which is just one of many Trump has ordered since the presidential election. He's purged several major defense officials since Nov. 3, including former Defense Secretary Mark Esper. 

"It is alarming and yet unsurprising that President Trump fired Director Krebs after he affirmed that there was no fraud in the 2020 election – a truth that President Trump refuses to accept," Hoyer said. 

But a senior DHS official told Fox News Krebs was “out of his lane” regarding election fraud allegations in CISA statements and on the agency’s “rumor control” website.

While CISA was successful in preventing election interference via a cyber attack on election infrastructure during the 2020 election, this DHS official says election fraud is different than election interference, and outside the scope of CISA’s authorities.

“CISA does not have first hand information on allegations of voting fraud or investigate such claims, responsibility for which lies with State and local authorities and the Department of Justice,” according to the DHS official, who adds, “Allegations of voter fraud are being adjudicated through the court system.”

CISA Released a statement last week, calling the 2020 election, “The most secure in history...” The statement goes on, “There is no evidence that any voting system deleted or lost votes, changed votes, or was in any way compromised.” 

This DHS official calls the latter part of that statement too broad, specifically the phrase, “or was in any way compromised.”

“CISA is responsible for infrastructure and cyber security, not the voting system, which would include mail-in ballots and all kinds of other matters which are clearly outside of their equity,” said the DHS official.

There are also some entries on CISA’s Rumor Control web page which seem specifically aimed instances of voter fraud allegations, which are outside of CISA’s responsibilities, according to this DHS official.

Fox News has reached out Krebs on the matter. He has not yet responded to our inquiries.

It is not universally accepted that there was no fraud in the presidential election. In fact, most experts believe that there was at least some. But the amount of fraud, experts have said, was almost certainly so marginal that it could not change the result in even one of the states critical to the electoral college that Trump is losing in by tens of thousands of votes. Trump would need the result to change in multiple states as Joe Biden is currently well over the 270 electoral votes needed to win the presidency. 

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The Trump campaign, meanwhile, has continued to insist that there are enough irregularities to change the results of states in favor of Trump. A Tuesday press release from the campaign cited a report by the Atlanta Journal-Constitution that 2,600 new votes were found during Georgia's hand recount. 

“The Trump campaign has amassed a significant amount of evidence of voter fraud from the November 3rd election and we continue to collect information,” Trump personal attorney Rudy Giuliani said in a statement. “We continue to do everything possible to uncover and combat this fraud, so every lawful vote is counted and every unlawful vote is not counted."

Trump, as of Wednesday morning as Georgia nears the end of its recount, is losing in the state by nearly 14,000 votes. 

"If he thinks he can simply say ‘you’re fired!’ to every official who refuses to go along with his post-election temper tantrum, he will find himself lonelier and lonelier over the next 64 days," Hoyer also said. "More importantly, he risks doing lasting damage to our national security and our democracy the longer he refuses to accept the election results, blocks the formal transition, and removes officials in critical positions. It is time for President Trump to accept reality and acknowledge President-elect Biden as his successor."

House Speaker Nancy Pelosi, D-Calif., also slammed the president late Tuesday, calling Trump's actions a "dangerous and shameful charade" while emphasizing the need for action on the coronavirus pandemic. Pelosi also praised Krebs as "a deeply respected cybersecurity expert who worked diligently to safeguard our elections, support state and local election officials and dispel dangerous misinformation."

Dissension also came from within the ranks of the Republican Party, specifically from Sen. Ben Sasse, R-Neb., who has a history of disagreeing with the president. 

"Chris Krebs did a really good job — as state election officials all across the nation will tell you — and he obviously should not be fired," Sasse said in a statement. "I’m particularly grateful for the work he did on the Cyber Solarium Commission to help the nation prepare for the future of war."

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Sen. Richard Burr, R-N.C., also publicly disagreed with Trump. 

"Chris Krebs is a dedicated public servant who has done a remarkable job during a challenging time. Chris and his team at CISA have worked diligently to strengthen our election infrastructure, helping to shore up vulnerabilities and build trust between state and federal governments," Burr said.

He added: "The creative and innovative campaign CISA developed to promote cybersecurity should serve as a model for other government agencies. Their efforts were essential in protecting the 2020 U.S. presidential election against threats of foreign interference."

The president's lawsuits and recount efforts have, for the most part, failed to uncover evidence of voting irregularities. And when they do, the irregularities haven't been enough to sway the results in states.

The vote-counting saga is likely to come to an end in the coming weeks as states are required to resolve their electoral controversies by early December and presidential electors will vote on Dec. 14, slightly less than a month from Wednesday. 

Fox News' Thomas Barrabi, Madeleine Rivera, Chad Pergram and Mike Emanuel contributed to this report.