Gambian President Yahya Jammeh is refusing to step down despite the threat of military intervention by neighbouring states.
Adama Barrow, who beat him in elections last month, is due to be inaugurated as the new president on Thursday, but Mr Jammeh has ignored the deadline.
West African military forces are ready to enforce a transfer of power.
Mauritanian President Mohamed Ould Abdel Aziz failed to break the deadlock at last-minute talks with Mr Jammeh.
Mr Abdel Aziz flew in to the Gambian capital Banjul on Wednesday evening to meet Mr Jammeh before flying on to Dakar airport for further discussions with Mr Barrow and Senegal's President Macky Sall.
"I am now less pessimistic [that Mr Jammeh] will work on a peaceful solution that is in the best interest for everyone," Mr Abdel Aziz said.
Senegalese troops remain stationed at the Gambian border, despite the deadline for Mr Jammeh to stand down passing at midnight.
The threat of military action is supported by Nigeria and other states in the region.
However, Gambian army chief Ousman Badjie said his troops would not fight Senegalese forces should they enter into the country, AFP news agency reports.
"We are not going to involve ourselves militarily, this is a political dispute," he said. "I am not going to involve my soldiers in a stupid fight. I love my men."
Mr Jammeh has ruled The Gambia since taking power in a coup in 1994.
Wednesday was meant to be his last day in office but parliament granted him three more months in the post.
Mr Barrow, who was said to be preparing to be sworn in as president "on Gambian soil" on Thursday, remains in neighbouring Senegal.
At least 26,000 Gambians, fearful that violence could erupt, sought refuge in Senegal this week.
Meanwhile, thousands of UK and Dutch tourists continue to be evacuated from the tiny West African state on special charter flights. Gambia is a popular beach destination among European holidaymakers, especially in winter.
Why is Mr Jammeh refusing to leave office?
Mr Jammeh initially accepted that Mr Barrow had won the election but later reversed his position and said he would not step down.
He declared a 90-day state of emergency calling for "peace, law and order" after what he said were irregularities in the election process.
He said that along with errors made by the electoral commission, some of his supporters were turned away from polling stations.
The commission later accepted that some of the results it initially published contained errors, but said they would not have affected Mr Barrow's win.
Mr Jammeh has said he will stay in office until new elections are held.
Retaining power would also ensure he was not prosecuted in The Gambia for alleged abuses committed during his rule.
Why is Senegal taking the lead?
Ecowas, the Economic Community of West African States (Ecowas), mandated Senegal because it almost surrounds The Gambia.
Col Abdou Ndiaye, a spokesman for the Senegalese military, said Ecowas had decided on the deadline to try to achieve a diplomatic solution.
"Things are getting into place and Ecowas forces are ready to intervene if needed after midnight if we can't find a diplomatic solution to the Gambian crisis," he said.
The Ecowas force is seeking UN Security Council endorsement to use "all necessary measures" to help remove Mr Jammeh.
The Gambia's entire armed forces are made up of only about 2,500 troops, making it difficult to see how they can defeat a regional force if it moves in, says BBC Africa Monitoring security correspondent Tomi Oladipo.
Nigeria says it sent fighters and other aircraft, along with 200 personnel, to Senegal on Wednesday morning.
Nigerian navy vessels are also on standby and a warship that sailed from Lagos on Tuesday will have the task of evacuating Nigerian citizens while putting on a show of force.
Ground troops are also being provided by Ghana.