Ghani left for Tajikistan, a senior Interior Ministry official said. The move comes as the Taliban entered the outskirts of Kabul but apparently remained outside of the city's downtown.
Afghan President Ashraf Ghani has said that he had fled the country on Sunday to "prevent a flood of bloodshed", as the Taliban entered the capital.
Ghani, who did not say where he had gone, said he believed "countless patriots would be martyred and the city of Kabul would be destroyed" if he had stayed behind.
"The Taliban have won... and are now responsible for the honour, property and self-preservation of their countrymen," he said in a statement posted to Facebook.
A senior Afghan Interior Ministry official said Ghani had left for Tajikistan.
But, according to a report on Al Jazeera, Ghani, his wife, his chief of staff and national security adviser had left the country for Tashkent, Uzbekistan.
The news channel cited a personal bodyguard of the president.
A representative of the Taliban said the group was checking on Ghani's whereabouts.
Pentagon authorises additional troops
American diplomats were being evacuated from their embassy by chopper after a swift advance, who were poised to run Afghanistan again 20 years after they were toppled by US-led forces following the September 11 attacks on the United States.
The Pentagon authorised an additional 1,000 troops to help with the evacuation from Kabul, a US official said on Sunday, bringing the total number of troops expected in Afghanistan temporarily to 6,000.
The official, speaking on condition of anonymity, said the additional 1,000 troops would come from the 82nd Airborne Division, which had already been on standby.
Taliban fighters 'on standby'
Taliban fighters were reaching the capital "from all sides", Afghan officials said.
But there were no reports of fighting and the group's spokesman Zabihullah Mujahid said they were waiting on the outskirts and were in talks with the Western-backed government for a peaceful surrender.
"Taliban fighters are to be on standby on all entrances of Kabul until a peaceful and satisfactory transfer of power is agreed," he said.
Representatives from the two sides were due to meet in Qatar on Sunday, Fawzi Koofi, a member of the Kabul negotiating team, said.
A source familiar with the matter said they would discuss a transition of power and US officials would also be involved.
'Their lives are safe'
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 said.
The ease of the Taliban's advance, despite billions of dollars spent by the US 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.
Before news that Ghani had left Kabul, a palace official said he was in emergency talks with US peace envoy Zalmay Khalilzad and officials from the NATO transatlantic alliance.
'Fear of fighting'
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".
READ MORE: Avoiding a final stand in Kabul
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.
After US-led forces withdrew the bulk of their remaining troops in the last month, the Taliban campaign accelerated as the Afghan military's defences appeared to collapse.
President Joe Biden on Saturday authorised the deployment of 5,000 US troops to help evacuate citizens and ensure an "orderly and safe" drawdown of military personnel.
Biden said his administration had told Taliban officials in talks in Qatar that any action that put US personnel at risk "will be met with a swift and strong US military response".
He has faced rising domestic criticism after sticking to a plan, initiated by his Republican predecessor Donald Trump, to end the US military mission in Afghanistan by August 31.
"An endless American presence in the middle of another country's civil conflict was not acceptable to me," Biden said on Saturday.