Afghanistan’s President Ashraf Ghani has held urgent talks with local leaders and international partners as Taliban rebels pushed closer to Kabul, capturing a town south of the capital that is one of the gateways to the city.

The United States and other countries rushed in troops to help evacuate their embassies after the militants captured town after town as US and other foreign forces who have backed the government withdrew.

Many Afghans have fled to Kabul, driven out by fighting and fearful of a return to hardline Islamist rule.

“As your president, my focus is on preventing further instability, violence, and displacement of my people,” Ghani said in a brief televised address, adding that he was consulting government, elders, politicians and international leaders.

He gave no sign of responding to a Taliban demand that he resign for any talks on a ceasefire and a political settlement, saying his priority remained the consolidation of the country’s security and defence forces.

“Serious measures are being taken in this regard,” he said, without elaborating.

He spoke soon after the insurgents, facing little resistance, took Pul-e-Alam, capital of Logar province and 70 km south of Kabul, according to a local provincial council member, who spoke to Reuters on condition of anonymity.

The gain of the city, a staging post for a potential assault on Kabul, comes a day after the insurgents took the country’s second- and third-biggest cities.

The Taliban says it is close to capturing Maidan Shahr, another town close to Kabul on the main highway to the southern hub of Kandahar.

American troops have begun flying in to Kabul to help in the evacuation of embassy personnel and other civilians, a US official said on condition of anonymity.

The Pentagon said two battalions of Marines and an infantry battalion will arrive in Kabul by Sunday evening, involving about 3000 troops. An infantry brigade combat team will move to Kuwait to act as a quick reaction force for security in Kabul if needed.

Britain and several other Western nations are also sending troops as resistance from Afghan government forces crumbles and fears grow that an assault on Kabul could be just days away.

An Afghan government official confirmed on Friday that Kandahar, the biggest city in the south, was under Taliban control as US-led international forces complete their withdrawal after 20 years of war.

Herat in the west, near the border with Iran, also fell to the group.

Kandahar’s loss was a heavy blow to the government. It is the heartland of the Taliban – ethnic Pashtun fighters who emerged in 1994 amid the chaos of civil war – and is close to the town of Spin Boldak, one of the two main entry points into Pakistan and a major source of tax revenues.

Some embassies have begun to burn sensitive material ahead of evacuating, diplomats said.

Many people in the capital were stocking up on rice and other food as well as first aid, residents said. Visa applications at embassies were running in the tens of thousands, officials said, and Washington was asking countries to temporarily house Afghans who worked for the US government.

The explosion in fighting has raised fears of a refugee crisis and a rollback of gains in human rights, especially for women.

Some 400,000 civilians have been forced from their homes this year, 250,000 of them since May.

Of Afghanistan’s major cities, the government still holds Mazar-i-Sharif in the north and Jalalabad, near the Pakistani border in the east, in addition to Kabul.

The speed of the Taliban’s gains has led to recriminations over the US withdrawal, which was negotiated last year under the administration of President Joe Biden’s Republican predecessor, Donald Trump.

Biden said this week he did not regret his decision to follow through with the withdrawal. He noted Washington has spent more than $US1 trillion ($A1.4 trillion) and lost thousands of troops over two decades, and called on Afghanistan’s army and leaders to step up.

Opinion polls showed most Americans back Biden’s decision, but Republicans criticised the Democratic president’s handling of the US withdrawal.