The US military mission in Afghanistan will end on August 31, President Joe Biden announced Thursday, as Afghan commandos battled the Taliban for control of a provincial capital in the most brazen assault by the militants since Washington stepped up its troop withdrawal.

Nearly 20 years after it invaded in the wake of the 9/11 attacks, the US military has "achieved" its goals in the country, killing Osama bin Laden, degrading Al-Qaeda and preventing more attacks on the United States, Biden said in a White House speech.

"We are ending America's longest war," he said.

"The status quo is not an option," Biden said of staying in the country. "I will not send another generation of Americans to war in Afghanistan."

"The United States cannot afford to remain tethered to policies created to respond to a world as it was 20 years ago," he said. "We need to meet the threats where they are today."

Biden said the United States "did not go to Afghanistan to nation-build" and that the Afghan people alone should determine their future.

But he acknowledged the uncertainty about what that future would look like.

Asked if a Taliban takeover was "inevitable," the president said: "No, it is not."

But, he admitted, "the likelihood there is going to be one unified government in Afghanistan controlling the whole country is highly unlikely."

"The Afghan government... has to come together," the president said. "They clearly have the capacity to sustain the government in place. The question is, will they generate the kind of cohesion to do it?"

He expressed faith in Afghan forces, who for years have been trained by and received equipment from the United States, against the resurgent Taliban.

"I do not trust the Taliban," Biden said, "but I trust the capacity of the Afghan military."

And he flatly rejected comparisons with the US experience in Vietnam.

"The Taliban is not the North Vietnamese army," Biden said. "They're not remotely comparable in terms of capability."

"There's going to be no circumstance where you are going to see people being lifted off the roof of an embassy of the United States from Afghanistan," he added. "It is not at all comparable."

Fighting rages

Biden's address came as fighting raged for a second straight day in the capital of Afghanistan's Badghis province, with residents either fleeing the city or barricading themselves in their homes.

Plumes of smoke billowed over Qala-i-Naw, soundtracked by gunfire as the insurgents fought hundreds of Afghan commandos rushed to the city overnight.

Qala-i-Naw resident Aziz Tawakoli said Taliban fighters were still roaming the city.

"You can see them going up and down the streets on their motorcycles," he said.

Badghis health official Abdul Latif Rostaee said at least 10 civilians had been taken to hospital since the fighting erupted.

"Our security forces are bravely fighting them and the enemy is being pushed back," Badghis Governor Hessamuddin Shams told AFP on Thursday. "They are fleeing. We will give a hard blow to the enemy."

Badghis provincial council member Zia Gul Habibi said the Taliban had suffered casualties, but also surrounded the city.

"All districts are under their control... People are really in fear," she said. Afghan civilians have long paid an outsized price in the fighting.

Since the US ramped up its withdrawal -- which the Pentagon has said is 90 percent complete -- the Taliban have launched a blistering campaign to capture new territory, and fears are mounting that Afghan forces will collapse without vital American air support.

President Ashraf Ghani said the government had the capacity to handle the situation, but admitted difficulties lay ahead.

"What we are witnessing is one of the most complicated stages of the transition," he said in a speech in Kabul.

"Legitimacy is ours; God is with us."

Taliban victory?

In London, Prime Minister Boris Johnson said most British troops had left Afghanistan, as part of a NATO withdrawal in parallel to the US pullout.

The Taliban, meanwhile, appear to be pressing for a full military victory.

Supposed peace talks between the insurgents and the government in Doha have largely fizzled out after months of deadlock, and the Taliban have captured dozens of new districts since early May.

Human Rights Watch said the insurgents were forcing people from their houses in northern areas that they had captured.

Biden pledged to continue supporting the Afghan government and security forces and said thousands of Afghan translators who worked for US forces and face threats from the Taliban would be able to find refuge in the United States.

"There is a home for you in the United States, if you choose," he said. "We will stand with you, just as you stood with us.