Afghan President Ashraf Ghani says he will not give up the achievements of the last 20 years and that consultations are underway.

He delivered a brief and vague televised address on Saturday, his first public appearance in days following a major Taliban advance.

"As your President, my focus is on preventing further instability, violence, and displacement of my people," Ghani was quoted by Reuters as saying.

"We have started consultations, inside the government with elders and political leaders, representatives of different levels of the community as well as our international allies," he said. "Soon the results will be shared with you, he added, without elaborating further.

According to Reuters, Ghani gave no sign of responding to a Taliban demand that he resign for any talks on a ceasefire and a political settlement, saying "re-integration of the security and defence forces is our priority, and serious measures are being taken in this regard".

The president had flown to Mazar-e-Sharif on Wednesday to rally the city's defences, meeting with several militia commanders, including Abdul Rashid Dostum and Ata Mohammad Noor, who command thousands of fighters.

They remain allied with the government, but during previous rounds of fighting in Afghanistan, warlords have been known to switch sides for their own survival. Ismail Khan, a powerful former warlord who had tried to defend Herat, was captured by the Taliban when the insurgents seized the western city after two weeks of heavy fighting.

The insurgents have seized most of northern, western and southern Afghanistan and are battling government forces some 11 kilometers (7 miles) south of Kabul.

The United States is set to withdraw its last forces by Aug. 31, raising questions about the survival of Ghani's Western-backed government.

The U.S. invaded Afghanistan after the 9/11 attacks nearly 20 years ago.

The Taliban seized a province just south of Afghanistan's capital and launched a multi-pronged assault early Saturday on a major city in the north defended by powerful former warlords, Afghan officials said.

The insurgents have captured much of northern, western and southern Afghanistan in a breakneck offensive less than three weeks before the United States is set to withdraw its last troops, raising fears of a full militant takeover or another Afghan civil war.

The Taliban captured all of Logar and detained its provincial officials, Hoda Ahmadi, a lawmaker from the province, said Saturday. She said the Taliban have reached the Char Asyab district, just 11 kilometers (7 miles) south of the capital, Kabul.

The Taliban also attacked the northern city of Mazar-e-Sharif from several directions, setting off heavy fighting on its outskirts, according to Munir Ahmad Farhad, a spokesman for the provincial governor. There was no immediate word on casualties.

American troops have begun flying in to Kabul to help in the evacuation of embassy personnel and other civilians, a U.S. official said.

The Pentagon has said two battalions of Marines and one infantry battalion will arrive in Kabul by Sunday evening, involving about 3,000 troops.

"They have arrived, their arrival will continue 'til tomorrow," the official told Reuters on condition of anonymity.

An infantry brigade combat team will also move out of Fort Bragg, North Carolina, to Kuwait to act as a quick reaction force for security in Kabul if needed, the Pentagon has said.

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.