Teresa Dailey, a prominent Florida Republican fundraiser and Trump supporter who attended the private event, told CNN on Sunday that Graham called on Republicans to unite as a party and support the presumptive GOP nominee to defeat Hillary Clinton in the general election.
"He did say that we need to get behind him," Dailey said Sunday.
Graham on Monday disputed that characterization of his remarks, telling CNN that he is supporting neither Trump nor Clinton and that "nothing's changed."
He added that he focused on the House and Senate races, but did say that he told donors that he "enjoyed" his recent phone conversation with Trump.
Dailey acknowledged Monday that Graham did not specifically call on Republicans to "get behind Donald Trump, exactly," but that "we need to get behind the party and support the party and do what we need to do to raise the funds necessary to make sure that Donald J. Trump is our next president of the United States."
Graham also told CNN's Dana Bash that he told donors that he will no longer pick a fight with Trump because it does no good.
The fundraiser, Graham said, was to help him retire debt from his presidential campaign. It was hosted by former U.S. Ambassador to Portugal Al Hoffman, a former Republican National Committee finance chairman who also co-chaired Sen. John McCain's 2008 presidential bid.
Graham spokesman Kevin Bishop repeatedly declined opportunities Sunday to characterize Graham's comments, simply confirming that Graham doesn't support a third-party run that some conservatives are working to organize and that Graham's position on the presidential race has not changed.
"There hasn't been any change in his position," Bishop said. "He's been pretty upfront and outspoken."
Dailey said Graham reiterated Saturday that he has no plans to formally endorse Trump because it would not necessarily help Trump.
Graham has been among Trump's most vocal and fiercest critics but has warmed to the New York real estate mogul since the two spoke over the phone earlier this month.
Graham described the call as a "cordial, pleasant phone conversation" and said the two discussed national security threats, including ISIS.
"My criticism has been wide and it's been deep, but we did have a good conversation. He asked good questions," Graham said Friday on CNN, though he declined to offer a formal endorsement of Trump over Clinton.
Graham said at the fundraiser Saturday that he has now spoken with Trump several times to discuss foreign policy, Dailey said.
Graham has offered some of the most biting criticisms of Trump, including calling him a "race-baiting, xenophobic, religious bigot" late last year.
And after Trump locked up the Republican nomination early this month, Graham said that Trump doesn't have the temperament or judgment to be president and said Trump has "conned" the Republican Party.