Forces loyal to the UN-backed president of Ivory Coast, Alassane Ouattara, are pressing on the main city of Abidjan and are closing in on his presidential rival, Laurent Gbagbo.
Some police units and the head of the army have defected from Mr Gbagbo.
The UN says Mr Gbagbo lost last year's election to Mr Ouattara, but he has so far refused to cede power.
UN troops in the country have now taken control of Abidjan airport, officials from the organisation said.
Armed supporters of Mr Gbagbo have been patrolling districts of the city, setting up roadblocks.
The BBC's Valerie Bony in Abidjan says there have been fierce clashes around the national television centre in a residential part of the city, and heavy weapons fire in northern suburbs.
She says an informed source had told her that Edouard Kassarate, the head of the gendarmerie or military police, had defected to the Ouattara side and had gone to the Hotel de Golf, Mr Ouattara's headquarters in Abidjan, which had been besieged by Mr Gbagbo's forces.
The UN envoy in Abidjan, Choi Young-jin, told French radio the blockade of the hotel was no longer in place as pro-Gbagbo units had left.
It is believed that the police and the paramilitary gendarmerie have gone over to Mr Ouattara, leaving only the presidential guard and militia forces defending Mr Gbagbo.
Mr Gbagbo's army chief, Phillippe Mangou, earlier defected, seeking refuge at the home of South Africa's ambassador in Abidjan.
Reuters news agency reported that heavy weapons and machine guns were heard firing in central Abidjan, in two districts near the presidential palace - still controlled by the presidential guard.
French forces were seen in armoured vehicles in the city, possibly to protect French nationals from any violence. Ivory Coast, like many former French colonial possessions, hosts a French military base.
There have been reports of looting in some districts of the city.
Mr Ouattara's officials declared an overnight curfew for Abidjan to run from Thursday until Sunday and said the country's land, sea and air borders would be closed "until further notice".
The head of Mr Ouattara's parallel government, Guillaume Soro, said Mr Gbagbo had only a few hours left in power.
"The game is over for Gbagbo. It is finished," he told Reuters in Yamoussoukro, Ivory Coast's capital.
The international community, including UN chief Ban Ki-moon and France, has urged Mr Gbagbo to immediately cede power to Mr Ouattara.
The US urged both sides to exercise restraint and protect civilians.
US Assistant Secretary of State Johnnie Carson said both Mr Gbagbo and his wife would be held accountable if significant violence broke out.
Mr Ouattara was internationally recognised as president last year, after the electoral commission declared him winner of the November run-off vote.
The UN, which helped organise the vote, certified it as legitimate.
However, Mr Gbagbo claimed victory after the Constitutional Council overturned Mr Ouattara's win.
The forces supporting Mr Ouattara have made lightning advances since Monday, moving out from their base in the northern half of the country.
On Wednesday, his fighters captured Ivory Coast's capital, Yamoussoukro, and the key port of San Pedro.
Mr Gbagbo's hometown of Gagnoa has also fallen.
In a televised address earlier on Thursday, Mr Ouattara appealed for his rival's soldiers to join him in order to prevent further suffering.
Since the crisis began in December, one million people have fled the violence - mostly from Abidjan - and at least 473 people have been killed, according to the UN.
Sanctions and a boycott on cocoa exports in what is the world's biggest producer of cocoa beans have brought West Africa's second-biggest economy to its knees, with banks closed for more than a month.
An armed rebellion in 2002 split the nation in two - a division the elections were meant to heal.