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Some Republicans are insisting that Americans wait for vote counts to be finalized and certified after the Fox News Decision Desk projected that President-elect Biden will beat President Trump and become the 46th president of the United States, while others congratulated Biden on his win Saturday.

Biden is the oldest person ever elected president of the United States. He joins a club of men to hold both the presidency and the vice-presidency that includes Theodore Roosevelt, Richard Nixon, George H.W. Bush and Thomas Jefferson. Vice President-elect Harris will be the first woman and the first person of color to hold that office. 

But Sen. Josh Hawley, R-Mo., on Saturday panned media projections that favor Biden and said Americans should wait for recounts and legal challenges before declaring who will be president come Jan. 20. 

"The media do not get to determine who the president is," Hawley said. "The people do. When all lawful votes have been counted, recounts finished, and allegations of fraud addressed, we will know who the winner is."

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Sen. Lindsey Graham, R-S.C., appeared to address the race calls in favor of Biden with a statement sent early Wednesday afternoon on an affidavit he received from the Trump campaign on potential Post Office misconduct in Pennsylvania. 

"Election outcomes are not determined by media outlets but certified, accurate vote counts," Graham said of an affidavit from a postal worker that accused other postal workers of backdating mail ballots. "Officials in Pennsylvania should take allegations from Mr. Hopkins and others seriously before certifying a final outcome."

But legal action from the Trump campaign or recounts are highly unlikely to close the margins that Biden has opened up in Pennsylvania and Nevada -- which are the calls that put Biden over 270 electoral votes, the number needed to win the presidency -- and in other states that have been called by the Fox News Decision Desk. Even if some misconduct or fraud is found, and some votes are changed or thrown out, it appears impossible that any such challenges could close the gaps between Biden and Trump in those states, based on the history of past recounts and legal challenges. 

Nevertheless, Trump, who was playing golf Saturday when Fox News and other media organizations called the race, released a statement through his campaign saying that Biden should not be declaring victory. 

"We all know why Joe Biden is rushing to falsely pose as the winner, and why his media allies are trying so hard to help him: they don’t want the truth to be exposed," a statement from Trump read. "Beginning Monday, our campaign will start prosecuting our case in court to ensure election laws are fully upheld and the rightful winner is seated. The American People are entitled to an honest election: that means counting all legal ballots, and not counting any illegal ballots."

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Meanwhile, a number of other Republicans congratulated the new president-elect on his victory, including former GOP presidential nominee Mitt Romney and potential 2024 presidential contender Larry Hogan, the governor of Maryland. 

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"Ann and I extend our congratulations to President-elect Joe Biden and Vice President-elect Kamala Harris," Romney said in a statement. "We know both of them as people of good will and admirable character. We pray that God may bless them in the days and years ahead."

Added Maryland's Republican Gov. Larry Hogan: "Congratulations to President-elect Biden. Everyone should want our president to succeed because we need our country to succeed. We have great challenges ahead of us as a country. Now more than ever, we need to come together as Americans."

Ari Fleischer, the former press secretary for George W. Bush, said "congratulations to President-elect Joe Biden" on Fox News Saturday afternoon.

"Congratulations to President-elect Biden. I have prayed for our President most of my adult life," Jeb Bush, the former Republican governor of Florida and 2016 GOP presidential primary candidate said. "I will be praying for you and your success. Now is the time to heal deep wounds. Many are counting on you to lead the way."

Sen. Lamar Alexander, R-Tenn., took a more measured tone Saturday while emphasizing respect for the results of the election. 

"After counting every valid vote and allowing courts to resolve disputes, it is important to respect and promptly accept the result," Alexander said. "The orderly transfer or reaffirming of immense power after a presidential election is the most enduring symbol of our democracy."

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Alexander's tone reflected a statement from Senate Majority Leader Mitch McConnell, R-Ky., which was released Friday.

"Here’s how this must work in our great country: Every legal vote should be counted. Any illegally-submitted ballots must not. All sides must get to observe the process. And the courts are here to apply the laws & resolve disputes," McConnell said. "That's how Americans' votes decide the result."

McConnell's office stood by that statement Saturday and said it does not have anything to add to that comment. 

Fox News' Jason Donner contributed to this report.