Graham was responding to 2020 presidential candidate Joe Biden's harsh criticisms over Graham's decision to investigate Hunter Biden's role at a Ukrainian gas company.
Graham said that while he likes Biden and considers him a "decent fella," he claims the new investigation into Biden's son has nothing to do with his friendship with the former vice president.
"It is obvious to me that Hunter Biden did some things that need to be looked at," Graham said during an interview with radio host Brian Kilmeade of FOX News on Monday. "I'm going to make sure that those questions are asked."
In response, Biden campaign spokesman Andrew Bates said, "Republicans controlled both chambers of Congress for most of the last five years and said or did nothing to indicate they thought that this warranted attention."
Last week, in an interview with CNN, Biden slammed Graham, a once-close Republican ally and family friend.
"I am disappointed, and quite frankly, I'm angered by the fact. He knows me. He knows my son. He knows there's nothing to this," Biden said. "Lindsey is about to go down in a way that I think he's going to regret his whole life."
"I say, Lindsey, I just -- I'm just embarrassed by what you're going for you. I mean, my, lord," Biden added.
Graham, who chairs the Senate Judiciary Committee and is a top Trump ally on Capitol Hill, requested records from the State Department on Thursday related to Biden's communications with then-Ukrainian President Petro Poroshenko on their alleged efforts to oust a Ukrainian prosecutor in 2016.
In his letter to Secretary of State Mike Pompeo, Graham is seeking records from February and March of 2016 related to former prosecutor Victor Shokin's firing. At the time, Biden's son Hunter held a board position with Burisma Holdings, a Ukrainian energy company, which was facing scrutiny from Shokin's office.
Witnesses in the impeachment hearings before the House Intelligence Committee, including the former U.S. special envoy to Ukraine, have refuted the allegations as baseless. Kurt Volker told the committee last week that he has known Biden as an honorable man for more than two decades.
"The allegations against Vice President Biden are self-serving and non-credible," Volker said.
Graham previously said calling in the Bidens as witnesses would amount to nothing but a "circus" in the Senate. But on Monday, he doubled down, later telling reporters in South Carolina that his "conscience is clear."
"I'm not going to create a country where only Republicans get investigated. There's a lot of corruption in Ukraine, they're an important ally. I thought Mueller would end this but Adam Schiff has created a process in the House that's un-American, dangerous to the presidency, and we're going to ask questions of Hunter Biden's role in getting the prosecutor fired," he went on.
"My friendships with these people are not going to keep me from asking questions that somebody needs to ask," Graham said of Biden. "I am doing this because somebody needs to do it."
He added, "My friendship with Joe Biden, if it can't withstand me doing my job, then it's not the friendship I thought we had. I admire him as a person, I think he's always tried to do right by the country. But as a person, I like him."