The Post obtained a recording of the call a day after Trump again attacked the integrity of Georgia's election count on Twitter, claiming - without evidence - that "political corruption" in one county was "rampant".
Raffensperger replied on Twitter: "Respectfully, President Trump: What you're saying is not true. The truth will come out."
During yesterday's often heated phone call, Trump urges Raffensperger to "find 11,780 votes," the Washington Post reports.
"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...
"There's no way I lost Georgia. There's no way. We won by hundreds of thousands of votes."
Georgia certified election results showing that President-elect Joe Biden won the state's November 3 election by 11,779 votes.
Georgia counted its votes three times in the wake of the election, confirming Biden's victory. That included a full recount by hand.
Raffensperger and the state's Republican Governor, Brian Kemp, certified the outcome, and Georgia's 16 electoral votes were officially cast for Biden in mid-December.
The President's frustration was evident during yesterday's call. He called Raffensperger a "child", said the Secretary of State was "either dishonest or incompetent", and warned he was taking a "big risk" by denying the theory about destroyed ballots in Fulton County.
"Tell me Brad, what are we going to do? We won the election, and it's not fair to take it away from us like this," he said.
"I think you have to say that you're going to re-examine it, and you can re-examine it. But re-examine it with people that want to find answers, not people who don't want to find answers."
In another moment, amid the barrage of allegations, Raffensperger suggested Trump's sources were less than credible.
"Mr President, the problem you have with social media, that – people can say anything."
"Oh, this isn't social media. This is Trump media," Trump replied.
Also on the line were White House Chief of Staff Mark Meadows, conservative lawyer Cleta Mitchell, and Raffensperger's legal counsel Ryan Germany.
Trump is due to travel to Georgia tomorrow for one final rally in support of Republican senators Kelly Loeffler and David Perdue.
No candidate in either of Georgia's Senate races won a majority of the vote on November 3, triggering a runoff on Wednesday NZT for both seats, with the top two candidates in each race facing off.
Control of the US Senate - which currently lies with the Republican Party - hinges on the outcome of these two races.
There was no widespread fraud in the presidential election, which a range of election officials across the country, as well as Trump's former attorney general, William Barr, have confirmed.
Nearly all the legal challenges from Trump and his allies have been dismissed by judges, including two tossed by the Supreme Court, which includes three Trump-nominated justices.
- With AP, news.com.au