And they repeatedly told Mr Trump that his claims were based on a string of false and debunked conspiracy theories.
Mr Trump even told Mr Raffensperger that he was taking “a big risk” in not pursuing his false claims.
"The people of Georgia are angry, the people in the country are angry,” said Mr Trump.
“And there’s nothing wrong with saying, you know, um, that you’ve recalculated.”
Mr Trump then was specific about what he was asking the politician, who has faced death threats from Trump supporters, to do.
“So look. All I want to do is this. I just want to find 11,780 votes, which is one more than we have. Because we won the state.”
Mr Trump insisted on the call that he had actually won the battleground state ahead of Mr Biden.
"There’s no way I lost Georgia,” Mr Trump repeatedly said.
“There’s no way. We won by hundreds of thousands of votes.”
The White House, the Trump campaign and Mr Raffensperger’s office have not responded to requests for comment.
The bizarre phone call came after 12 US senators and as many as 140 members of Congress said they planned on challenging the electoral college results in a joint session this week.
Mr Trump also warned the politician during the wild call that his treatment of the president would impact the state’s runoff election on Tuesday.
“You have a big election coming up and because of what you’ve done to the president - you know, the people of Georgia know that this was a scam,” said Mr Trump.
“Because of what you’ve done to the president, a lot of people aren’t going out to vote, and a lot of Republicans are going to vote negative, because they hate what you did to the president. Okay?
“They hate it. And they’re going to vote. And you would be respected, really respected, if this can be straightened out before the election.”
Democrats Jon Ossoff and Raphael Warnock are involved in tight races with Republicans David Perdue and Kelly Loeffler for the state’s now vacant senate seats.
The race, one of the most expensive in US history, will decide control of the US Senate, with Republicans maintaining power if they hold just one of the seats.
But if the Democrats manage to win both seats they will take control of the high chamber as vice president-elect Kamala Harris will break all ties after she is sworn in on 20 January.