The Taliban, an Islamist militant group that has seized large parts of Afghanistan, started entering the outskirts of Kabul on Sunday, local officials said.
Gunfire and sirens were heard sporadically across Kabul.
The Afghan capital is the last major city held by government forces after insurgents made several advances elsewhere this month amid the withdrawal of allied troops.
Taliban wants to avoid forceful takeover
The Taliban later pledged not to take the capital "by force."
"No one's life, property and dignity will be harmed and the lives of the citizens of Kabul will not be at risk," the militant group said in a statement.
Taliban spokesman Suhail Shaheen later told the Al-Jazeera English channel that they are "awaiting a peaceful transfer of Kabul city'' after they entered the capital's outskirts.
Shaheen declined to offer specifics on any possible negotiations between his forces and the government.
Matin Bek, the chief of staff to Afghan President Ashraf Ghani, wrote on social media: "Don't panic! Kabul is safe!"
The Taliban started an offensive nearly two weeks ago, capturing a number of key towns, cities and border posts.
US starts Kabul evacuation
Sunday's move on Kabul comes as international forces start to evacuate their diplomats amid the worsening security situation.
US intelligence officials said earlier this week that they believed it might take as long as three months for the Taliban to seize the Afghan capital.
Peace talks have been taking place in Doha, Qatar, since last September between the Afghan government and the Taliban.
But the negotiations, which are being mediated by the international community, have failed to bear fruit.
Taliban negotiators headed to presidential palace — report
The AP, citing an anonymous Afghan official, reports Taliban negotiators are making their way to the presidential palace for negotiations to facilitate a "transfer" of power.
The Afghan official said the goal was a peaceful hand over of the government to the Taliban.
Interior Minister Abdul Sattar Mirzakwal also said in a recorded speech that there would be "no attack on the city" and that "a peaceful transfer of power to the transitional government" was in the works, AFP reports.
Ghani wants stability
In a televised speech on Saturday, Afghan President Ashraf Ghani vowed that he would not give up the "achievements" of the past 20 years.
He warned that the country is in "serious danger" of facing "instability."
Ghani, an academic economist who spent most of his career in the United States, became president in 2014, winning a second term five years later.
