Republican Senator Shelby, Governor of Louisiana Edwards called on Americans to recognize Biden's victory and put the country "to the page".
"The Electoral College met earlier this week, it is our constitutional process to determine the outcome of the presidential election. The electors voted 306 votes for Joe Biden and 232 votes for Donald Trump.
"Although I wish the results would be different, it's about time we turn to a new page," he added.
John Bel Edwards, Governor of Louisiana, on the same day also urged people to quickly recognize Biden as President-elect, despite Republicans in the state congressional delegation opposing this.
"I am a lawyer. I know our courts exist to resolve disputes, but disputes need to be real," said Governor Edwards, a Democrat, said if there is evidence.
Edwards added he was sorry that State Attorney General Jeff Landry, a Republican member, supported the Texas lawsuit aimed at reversing President-elect Joe Biden's victory.
While avoiding direct criticism of President Trump, Governor Edwards noted that many state and federal courts across the country have denied cases of election fraud.
However, while Governor Edwards urged everyone to accept the results of the election, Republican members of the Louisiana parliamentary delegation still failed to admit Biden's victory.
Even when the electoral college on December 14 voted to confirm Biden is the President-elect, this group of Republicans still did not change their opinion.
Rep. Clay Higgins even attacked Biden's victory.
The offices of Republican Senators Steve Scalise, Mike Johnson, Ralph Abraham and Garret Graves are not currently responding to whether they will accept Biden's upcoming election results and inauguration.
Earlier, Senate Majority Leader Mitch McConnel congratulated Biden on his election, and asked Republican senators not to participate in efforts to reverse election results.
"Democracy works best when the losers admit defeat, leave gently and work together to ensure a smooth transition," said Governor Edwards.
On January 6, US Vice President and Senate President Mike Pence will preside over the plenary session of Congress to certify the electoral votes of each state, in alphabetical order.