January 19, 2017 0431 GMT
The appeal came at the 50th summit of the 15-member Economic Community of West African States (ECOWAS) in Nigeria, attended by 11 heads of state but without the leaders of four members including The Gambia, AFP reported.
Opposition leader Adama Barrow was declared winner of the December 1 polls and Jammeh initially conceded defeat, only to reverse his decision a week later, condemning "unacceptable errors" by election authorities and calling for a new vote.
Gambian security forces seized the country's Independent Electoral Commission earlier this week, drawing international condemnation.
On Saturday Liberian President Ellen Johnson-Sirleaf, the current ECOWAS chairperson, said in Abuja that the regional economic group would push for prompt resolution of the crisis.
"It is now important that the Authority, at this summit, considers recommended measures to bring this matter to successful conclusion before January 19, the constituted date when the mandate of the incumbent president expires," Sirleaf told the summit.
Mohamed Ibn Chambas, the UN top envoy for West Africa, said the global body would support efforts to resolve the election logjam.
"The UN remains concerned by some of the worrisome developments that occurred during the post election period in The Gambia," Chambas said after the summit was declared open by Nigerian President Muhammadu Buhari in his country's capital.
These included "in particular, the seizure of the headquarters of the Independent Electoral Commission by the Gambian military," he added.
On Tuesday, Sirleaf led a heavyweight delegation to The Gambia to seek to broker a deal, meeting both Jammeh and Barrow.
But Sirleaf announced at the end of the talks there was no deal.
The situation has been further complicated by Jammeh's political party filing a legal challenge against the result at the Supreme Court.
The African Union, the UN, local and international rights groups have asked Jammeh – who has been in power for 22 years – to step down.
Ahead of the ECOWAS summit, around 200 politicians, human rights activists and Gambian diaspora figures gathered in Dakar, capital of Senegal on Saturday to call for a peaceful transition of power in Gambia.
"We ask ECOWAS and the international community to ensure this choice is respected and to do all they can so that the democratic transition is not impeded," said a joint statement by Amnesty International, Article 19 and RADDHO rights groups.