"Our president should stand up and say, 'Hey, stand down people. This is the process," Graham told Fox News.
Graham also noted that the 2016 Democratic presidential nominee Hillary Clinton bears some responsibility for this situation as well.
"Hillary Clinton, if she had any class, and wasn't such a hypocrite as it related to her comments about not being or supporting a Democratic process. I mean, people are just standing back and letting this happen," Graham stated.
Electors in multiple US states have reported receiving threatening emails and phone calls.
Members of the Electoral College will meet in their US state capitols on Monday to cast a vote that will make President-elect Donald Trump's victory over Clinton official.
Trump won 306 electoral votes, 36 more than the 270 needed to win the presidential election.
A few electors are expected to defect and vote for a different candidate than the one their state voted for, but Trump is still expected to have enough electoral votes to become president.
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