Jammeh, who has ruled Gambia with an iron grip since a 1994 military coup, suffered a shocking loss after running for his fifth term.
In a December 2 address on Gambian state TV, Jammeh accepted his defeat and congratulated opponent Adama Barrow on his victory. But he now refuses to accept the outcome.
"I announce to you, Gambians, my total rejection of the election results and thereby annulling the elections in its entirety," Jammeh said in a televised speech Friday.
"We will go back to the polls because I want to make sure that every Gambian has voted under an independent electoral commission that is independent, neutral and free from foreign influence."
Jammeh had been expected to concede power to Barrow, with the country's electoral commission announcing last week the President would do so.
Barrow on Saturday said Jammeh has no authority to reject the election result. He appealed for calm and urged his rival to facilitate a smooth transition.
"I urge him to change his current position and accept the verdict of the Gambian people in good faith for the sake of the Gambia, our homeland, whose people deserve peace and freedom and prosperity," he said of Jammeh.
He added, "I wish to call on all Gambians to go about their business. We have impressed the world for delivering a free and fair and credible election. I am advising supporters of the coalition to celebrate the victory with discipline and maturity and prepare themselves for inauguration in January."
US: 'Unacceptable breach of faith'
The US government immediately criticized Jammeh's call for fresh elections.
"This action is a reprehensible and unacceptable breach of faith with the people of the Gambia and an egregious attempt to undermine a credible election process and remain in power illegitimately," the US State Department said in a statement.
"We call upon President Jammeh, who accepted the election results on December 2, to carry out an orderly transition of power to President-elect Barrow in accordance with the Gambian Constitution."
A spokesman for Human Rights Watch said the rights group was "deeply concerned" by reports of Jammeh's rejection of the results.
"The international community, notably ECOWAS and the African Union, should loudly protest any unlawful attempt to subvert the will of the Gambian people," said Babatunde Olugboji. ECOWAS is an acronym for the Economic Community of West African States, a bloc to which Gambia belongs.
Human rights groups have described Jammeh's 22-year regime as abusive, with hundreds of political prisoners languishing in jail. Jammeh also attracted heavy criticism for claiming he had created an herbal remedy for AIDS, and he once threatened to behead gay people.
Barrow, a property developer, won more than 45% of the vote with 263,515 ballots cast for him. Barrow once was a security guard at an Argos retail store in London where he once tackled a shoplifter, according to reports in UK newspapers.
On the eve and day of the elections, websites and phone lines were blocked. A heavy paramilitary presence was reported at poll stations as Gambians cast their votes using the country's unique marbles and drums system.
Human rights in the country have long been a topic of concern among international nongovernmental organizations. In April, the national organizing secretary of the United Democratic Party, or UDP, the country's largest opposition party, was beaten to death while in the custody of security services, according to a Human Rights Watch report.
The small West African nation is the fourth-largest source of migrants arriving in Italy
despite having a population of fewer than 2 million people.