Cautioning that he doesn't "believe it is appropriate for Congress to act based on a newspaper article," Graham said it's nevertheless that body's duty to "perform oversight regarding any potential campaign contacts between Trump officials and Russian intelligence officials."
"If they do exist, the contacts may have a logical explanation, but we will never know until Congress spends the time to investigate this matter," he said.
It was unclear from Graham's statement how Congress would confirm whether Trump campaign staff did indeed make contact with Russian officials before the election.
The senator suggested that Congress would be helping out the White House by surfacing details about any ties between Trump associates and Russia.
"The accusations regarding the Trump campaign’s ties to Russia are creating a cloud over the White House," he said in the statement. "They should be fairly investigated by the Congress in a bipartisan manner. It would serve the President’s interests to get to the bottom of this so he can move forward with his agenda."
Graham also gave a nod to calls from some conservatives to investigate leaks to the press about Trump aides' alleged contact with Russia.
"Any investigation should also include leaks coming from the White House and other government agencies," he said in the statement. "These leaks are damaging to our national security and the individuals involved must be punished."
Sen. Bob Corker (R-TN), chair of the Senate Foreign Relations Committee, also said Wednesday that Congress should probe Trump aides' communications with Russia.
"The base issue is getting to the bottom of what the Russian interference was and what the relationship was with associates of the Trump effort, and so that is the big elephant in the room that has got to be dealt with in the most appropriate way," he said on MSNBC's "Morning Joe."
"If I were them, by the way, if I were the people leading the Trump effort at the White House, I would want to make sure, with all of the suspicion, that everybody fully understood what has taken place, otherwise maybe there's a problem that obviously goes much deeper than what we now suspect," Corker added later.