"As you know, the Constitution does provide for federal oversight of state elections," the Fox News Sunday anchor told the GOP senator.
The South Carolina senator claimed no one was afraid of President Biden, but the "bad guys" feared Donald Trump.
Senator Lindsey Graham (R-S.C.) called Peter Daszak, a scientist on the team that traveled to Wuhan, "detached" from reality with how China works for trusting Chinese scientists.
The idea that the COVID-19 virus originated in a lab in China has gained renewed attention in recent weeks.
South Carolina Senator Lindsey Graham asked during a press conference Monday if there was a "deep state science department" that dismissed the Wuhan lab origins theory for COVID-19. He claimed people in the state department promoting the lab theory were silenced.
"All of this came from one Hamas rocket, one terrorist, who murdered a woman in Ashkelon," Cruz said at the end of the video he posted on Tuesday.
The former president has hinted at another run for the Republican Party's nomination two years from now.
Graham's comments came just days after Trump blamed "suppression polling" for reducing voter turnout during the 2020 election.
Graham echoed comments Israeli Prime Minister Benjamin Netanyahu made on Sunday and said he didn't see a two-state solution happening until Hamas is "marginalized."
"Is anybody in Russia afraid of hitting us again?" the Republican senator said.
The senator has previously said the Republican Party can't "move forward" without the former president.
The South Carolina senator has said he feels the Republican Party "can't grow" without the former president.
"If you don't win, the money is going to be used to take back the House and the Senate, so we can stop this slide to socialism," Graham said.
From 2015 to 2020, Black Americans were killed by police at a rate that was more than twice as high as white Americans.
The Republican senator called on his party to use "all the tools in the toolbox" to curb filibuster reform.
President Joe Biden stated he wants a complete withdrawal from Afghanistan by September 11, and Trump said that's "wonderful and positive." Graham referred to them as "generals" in his disagreement.
"I've never been more worried than I am now about the world at large," the Republican senator said.
"'General Biden' has been wrong about every military decision in recent memory," the South Carolina senator tweeted.
In the video, which was posted to Twitter by Jones, he can be heard saying, "Our Democracy is in crisis. The insurrection on January 6 made that clear. This crisis didn't arrive overnight, or by accident. The Supreme Court helped bring us here."
The military exit, Biden said, will begin May 1 and be completed by the 20th anniversary of the September 11 attacks.
Sen. Lindsey Graham (R-S.C.) said that President Joe Biden's plan to withdraw all U.S. troops from Afghanistan would be "paving the way for another 9/11" on Tuesday, calling his foreign policy decisions "completely incompetent and destabilizing."
The South Carolina Republican rallied against an assault rifle ban, saying "Democrats are basically declaring war on gun ownership."
The Republican senator largely defended the election legislation in Georgia, warning instead about Democrats' efforts to pass HR 1.
The Republican senator said any proposed ban on assault rifles would fail to win 60 votes.
The South Carolina senator told Fox News that GOP lawmakers would fight any Democratic plan to "abolish the filibuster and transform America."
Earlier this week, GOP Senator Tim Scott and CNN host Don Lemon, who are both Black, sparred over race, after Scott said that "woke supremacy" is as bad as "white supremacy."
The South Carolina senator told Fox News anchor Sean Hannity that border problems could be exploited by terrorists.
Senator John McCain's widow said the Republican Party is on the "brink" and will be forced to either "find its way or dissolve."
"It's just this bigger than life deal," Graham said about Trump. "He could make the Republican Party something that nobody else I know can make it. He can make it bigger, he can make it stronger, he can make it more diverse and he also could destroy it."
The Republican senator also said Trump had the power to make the party stronger and more diverse.