Georgia's Secretary of State Brad Raffensperger has said that matching the signature on absentee ballots to the signature on the outer envelopes was near-impossible because the two documents are separated to protect privacy.
In a tweet on Monday morning, Mr Trump called on the governor to overrule the secretary of state to do a match of signatures on ballots and envelopes.
"Why won’t Governor @BrianKempGA, the hapless Governor of Georgia, use his emergency powers, which can be easily done, to overrule his obstinate Secretary of State, and do a match of signatures on envelopes. It will be a “goldmine” of fraud, and we will easily WIN the state...." he said.
"....Also, quickly check the number of envelopes versus the number of ballots. You may just find that there are many more ballots than there are envelopes. So simple, and so easy to do. Georgia Republicans are angry, all Republicans are angry. Get it done!"
It comes a day after the president said he was ashamed to have endorsed Mr Kemp for Governor.
Appearing on Fox News Sunday night, Mr Trump told host Maria Bartiromo that "this character in Georgia" was a disaster, believed to be a reference to Mr Raffensperger - who the president called an "enemy of the people" on Thanksgiving.
“The governor’s done nothing, he’s done absolutely nothing. I’m ashamed I endorsed him," Mr Trump said.
The president also accused judges and electoral officials of "making deals", a continuation of his claims that Georgia officials are unable to verify signatures on absentee ballot envelops after the election because of the "consent decree" signed in March at the "urging" or former Democratic gubernatorial candidate Stacy Abrams.
According to an AP fact check of the allegation, there is nothing in the consent decree that prevents Georgia election clerks from scrutinizing signatures before the ballot and envelope are separated.
In his Fox News interview, Mr Trump continued to question the integrity of the Georgia election ahead of the January run-offs that would decide control of the Senate.
“Look at the election you have coming up right now. You're using the same garbage machinery, Dominion,” he said, in reference to Dominion Voting Systems.
Attorney L Lin Wood, who is working independently of the Trump campaign with Sidney Powell to file challenges to election results in Georgia, said a judge issued a restraining order on Sunday to prevent Georgia wiping Dominion voting machines.
"Defendants are hereby ENJOINED & RESTRAINED from altering, destroying, or erasing, or allowing the alteration, destruction, or erasure of, any software or data on any Dominion voting machine in Cobb, Gwinnett and Cherokee Counties," wrote US District Court Judge Timothy C Batten.
Mr Kemp and Mr Raffensperger, two defendants in the case, are arguing against making the Dominion machines available for forensic inspection due to “security and proprietary/trade secret” risks.
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