Afghanistan President Ashraf Ghani has left the capital Kabul for Tajikistan, a senior Afghan Interior Ministry official said on Sunday.
The president's office said it "cannot say anything about Ashraf Ghani's movement for security reasons".
A representative of the Taliban, which entered the capital Kabul earlier on Sunday, said the group was checking on Ghani's whereabouts.
Taliban insurgents entered Afghanistan's capital Kabul on Sunday and said they expected to take power within days, promising to moderate their earlier hardline Islamist rule even as foreign diplomats and many locals tried to leave.
American diplomats were evacuated from their embassy by chopper after a lightning advance by the militants, who were poised to run Afghanistan again following the Sept. 11 attacks on the United States.
Taliban fighters were reaching the capital "from all sides", a senior Afghan interior ministry official told Reuters.
However, there were no reports of fighting.
The group was in talks with the Western-backed government for a peaceful surrender, Taliban spokesman Zabihullah Mujahid said. "Taliban fighters are to be on standby on all entrances of Kabul until a peaceful and satisfactory transfer of power is agreed," he said in a statement.
Ali Ahmad Jalali, a US-based academic and former Afghan interior minister, could be named head of an interim administration in Kabul, three diplomatic sources said, though it was unclear whether the Taliban had agreed.
Known during their past rule for keeping girls out of school and their hardline practice of Islamic law, including punishments of amputation, stoning and hanging, the Taliban appear to be trying to project a more modern face.
Another spokesman Suhail Shaheen said the group would protect the rights of women, as well as freedoms for media workers and diplomats.
"We assure the people, particularly in the city of Kabul, that their properties, their lives are safe," Shaheen told the BBC, saying a transfer of power was expected in days.
The ease of the Taliban's advance, despite billions of dollars spent by the United States and others to build up local Afghan government forces, has stunned the world.
Just last week, a US intelligence estimate said Kabul could hold out for at least three months.
There was no immediate word on the situation from President Ashraf Ghani. A palace official said he was in emergency talks with US peace envoy Zalmay Khalilzad and officials from the NATO transatlantic alliance.
Power would be handed over to a transitional administration, the government's acting interior minister, Abdul Sattar Mirzakawal, tweeted on the Tolo news channel. "There won't be an attack on the city, it is agreed that there will be a peaceful handover," he said without elaborating.
A tweet from the Afghan presidential palace account said firing had been heard at a number of points around Kabul but that security forces, in coordination with international partners, had control of the city.
Many of Kabul's streets were choked by cars and people either trying to rush home or reach the airport, residents said.
"Some people have left their keys in the car and have started walking to the airport," one resident told Reuters by phone. Another said: "People are all going home in fear of fighting."
Afghans had fled the provinces to enter Kabul in recent days, fearing a return to hardline Islamist rule.
Early on Sunday, refugees from Taliban-controlled provinces were seen unloading belongings from taxis and families stood outside embassy gates, while the city's downtown was packed with people stocking up on supplies.