"If there's contacts between the Trump campaign and Russian intelligence officials outside the norm, that's not only big league bad, that's a game changer," Graham, R-S.C., said in an interview on "Good Morning America."
He continued, "Because if it is true, it is very very disturbing to me, and Russia needs to pay a price when it comes to interfering in our democracy and other democracies, and any Trump person who was working with the Russians in an unacceptable way also needs to pay a price."
Sources familiar with the matter confirmed to ABC News on Tuesday that U.S. authorities were probing communications between associates of Trump and suspected Russian intelligence officials before the presidential election.
The news comes one day after Trump's national security adviser, Michael Flynn, resigned amid questions about conversations he had with the Russian ambassador to the United States during the White House transition. In the days after Trump's inauguration, the Federal Bureau of Investigation interviewed Flynn to discuss his conversations with the Russian ambassador, according to multiple government officials.
The New York Times first reported the alleged "repeated contacts" between several of Trump's associates and Russians in the lead-up to the election. U.S. officials speaking with the newspaper noted, however, that there was no evidence of cooperation between the campaign and the Russians to attempt to influence the election.
Graham, a member of the Senate Committee on Armed Services, said there should be a "preliminary investigation," with members of Congress, including himself, overseeing the FBI's probe into the allegations. If the reports prove true, he said, Congress should "get to the bottom of this."
"I want to make sure myself that these intercepts exist, that the communications are outside the norm. If that's the case, it's time for Congress — in my view, the Senate — to do a joint select committee where we can look at it holistically," he said.
Trump took to Twitter this morning, saying of the allegations, tweeting, "The fake news media is going crazy with their conspiracy theories and blind hatred."
He wrote in another tweet, "This Russian connection non-sense is merely an attempt to cover-up the many mistakes made in Hillary Clinton's losing campaign."
In the wake of the allegations, Democrats argue Trump needs to release his tax returns so investigators can learn more about his dealings with Russia. Asked on "GMA" this morning if he agrees with this, Graham said, "Maybe so." But first, he said, he wants to know whether there was any "unacceptable" activity between the Trump campaign and Russians.
"If that is true, then we need to look into all things Russia when it comes to Trump, including his business ties, to help explain where he's coming from," Graham said. "And maybe none of it's true. But I can tell you this — that Congress is not fake. There are real members of Congress up here, Republicans and Democrats, who love our country and are going to make sure that checks and balance that have been in place for 200 years work even when the president is in your own party."
Graham, a former presidential candidate who dropped out of the race and then endorsed Republican presidential hopeful Jeb Bush, once said he could not "in good conscience" support Trump's candidacy. He told "GMA" that he won't judge Trump until the facts are clear.
"Donald Trump is an outlier when it comes to the Russians," Graham said. "Maybe it's just a policy difference. It's OK for Trump to disagree with Lindsey Graham and other Republicans on how to handle Russia. It would not be OK to have the Trump campaign receiving assistance from the Russians."
ABC News' Adam Kelsey, Meghan Keneally, Mike Levine and Cecilia Vega contributed to this report.