West African leaders gave Yahya Jammeh, who lost elections last month, until midday on Friday to hand over power and agree to leave Gambia or face military action carried out by the regional bloc ECOWAS.
Later however, Jammeh requested a four-hour extension until 4pm local time to cede, government sources said, according to the Reuters news agency.
It was not clear what he planned to do, though diplomats said his departure looked increasingly possible.
Red carpets were laid out at the airport in Gambia's capital in what appeared to be preparations for a speech by Jammeh and a departure.
Gambia's chief of defence forces Ousmane Badjie pledged his allegiance to the country's new president on Friday, a major shift amid continued mediation to persuade defeated Jammeh to cede power.
The leaders of Guinea and Mauritania met with Jammeh in Gambia on Friday.
West African troops entered the country to bolster new President Adama Barrow - who was sworn-in on Thursday - but military operations were suspended a few hours later in favour of a final diplomatic push to convince Jammeh, who has stubbornly refused to to exit peacefully.
In his first media interview with Al Jazeera, Barrow urged Jammeh to leave the country and said he hoped that the 15 ECOWAS countries can find him a safe haven.
"We cannot allow Yahya Jammeh to remain in Gambia, it will make our job difficult. That's why all our negotiations is he leave Gambia, he can later come back. But as of now the political climate doesn't allow that."
"I advise him in good faith to give peace a chance. It is about democracy."
Adama Barrow sworn in as Gambia's president in Senegal
Gambia's only land border is with Senegal. The regional coalition, which ECOWAS says involves 7,000 troops, entered from the southeast, southwest and north.
Jammeh started negotiations with ECOWAS on Thursday and agreed to step down. He demanded, however, an amnesty for any crimes that he may have committed during his 22 years in power and that he be permitted to stay in Gambia, at his home village of Kanilai.
Those demands were unacceptable, said Marcel Alain de Souza, head of ECOWAS.
Jammeh's continued presence in Gambia would "create disturbances to public order and terrorist movements," he said.
Support for the long-ruling leader has been crumbling. The army chief joined ordinary citizens celebrating in the streets on Thursday seven weeks after contested polls.
"Diplomacy is a long road - it always has been and always will be - so every opportunity to find a resolution is the best means possible for the region," Robin Sanders, former US ambassador to ECOWAS, told Al Jazeera.
"The last thing that West Africa needs is another conflict."
While there has been talk that a deal may include an amnesty for Jammeh, whose regime has been accused of various human rights abuses, Sanders said that this would set a bad precedent.
"I am not in the camp of complete amnesty because what you do is signal additional impunity going forward with other leaders, not only just in the continent but across the world," she said.
READ MORE: Gambia - Four ministers resign from Jammeh government
Barrow was sworn in at Gambia's embassy in Dakar, in neighbouring Senegal, on Thursday.
Celebrations erupted in Banjul, meanwhile, where tensions have run high over the crisis, especially since the declaration of a state of emergency by Jammeh made on Tuesday.
Barrow, a real-estate agent turned politician, had flown into Senegal on January 15 to seek shelter after weeks of rising tension over Jammeh's stance.
At least 46,000 people have fled Gambia for Senegal since the start of the crisis fearing unrest, the UN's refugee agency UNHCR said on Friday, citing Senegalese government figures.
Source: Al Jazeera and news agencies