The president made the remarks during a fractious press conference on Thanksgiving, where he claimed without evidence that massive voter fraud had taken place in the state.
Mr Trump said: “You're not allowed to harvest, but I understand the secretary of state, who is really an enemy of the people, the secretary of state, and whether he's Republican or not, this man, what he's done, supposedly he made a deal and you'll have to check this, where she is allowed to harvest but in other areas they're not allowed.”
The president has frequently called the press “enemies of the people" and has referred to Democrats as “enemies of the state".
Mr Trump and other Republicans have placed blame for the president's loss in Georgia on Mr Raffensperger. President-elect Joe Biden is the first Democrat to win the state since Bill Clinton in 1992.
The president has previously had high praise for Mr Raffensperger on Twitter.
"Brad Raffensperger will be a fantastic Secretary of State for Georgia - will work closely with @BrianKempGA. It is really important that you get out and vote for Brad..." Mr Trump wrote in 2018.
During his press appearance on Thursday, the president falsely accused Mr Raffensperger of working with Democrat Stacey Abrams, a lawyer, activist and former Georgia lawmaker, to permit "vote harvesting" in the state.
Ms Abrams has been credited with leading a registration drive that added 800,000 voters to the roll in Georgia ahead of the 2020 election.
That is entirely separate from ballot harvesting - in which voters complete an absentee ballot and give it to another person to drop off at a polling station. Under Georgia law, it is illegal for anyone to turn in another person’s ballot unless they are a close relative or live in the same home as the voter.
The president is not the only Republican who has turned his back on Mr Raffensperger.
In a column he wrote in USA Today on Wednesday, Mr Raffensperger said that Donald Trump threw him and his family "under the bus" even though they voted for him.
“This should be something for Georgians to celebrate, whether their favored presidential candidate won or lost. For those wondering, mine lost — my family voted for him, donated to him and are now being thrown under the bus by him,” Mr Raffensperger wrote.
Mr Raffensperger also accused Lindsey Graham,the senator from South Carolina, of asking him to disqualify thousands of legally cast, mail-in ballots by claiming their signatures were mismatched.
Ethics watchdogs have called on the Senate Ethics Committee to investigate whether Sen. Graham "threatened anyone with a Senate investigation of Georgia vote tally."
Mr Raffensperger has defended himself and the election in Georgia.
Mr Raffensperger said the election was "wildly successful and smooth" in his column.
When Mr Raffensperger certified the Georgia recount election last week, he reiterated his belief that the results were accurate.
“Working as an engineer throughout my life, I live by the motto that numbers don’t lie,” he said.
“As secretary of state, I believe that the numbers that we have presented today are correct. The numbers reflect the verdict of the people, not a decision by the secretary of state’s office or of courts or of either campaign.”