The Taliban have no plans to take the Afghan capital "by force," a spokesperson said in a statement on Sunday.
Taliban fighters took Jalalabad, near a major border crossing with Pakistan, earlier on Sunday, leaving Kabul as the last major city under government control.
There are conflicting reports on the situation in the Afghan capital.
Citing the Afghan Interior Ministry, Reuters reported that the Taliban have started entering Kabul "from all sides."
Meanwhile, a spokesman for the Taliban said that fighters were ordered Sunday to wait at the gates of Kabul and not enter the city, an insurgent spokesman said, after the complete collapse of the country's security forces.
"Core" U.S. team members were working from Kabul airport, Reuters reported citing a U.S. official, while a NATO official said several EU staff had moved to a safer, undisclosed location in the capital.