Afghan security forces "repelled" a coordinated Taliban assault on the northern city of Kunduz on Saturday, President Ashraf Ghani said, even as the insurgents claimed to have captured important city buildings.

The multi-pronged Taliban offensive on Kunduz, which has come under frequent attack since 2015, occurred as U.S. and insurgent negotiators continue to seek an agreement in Doha that would see thousands of American troops leave Afghanistan in return for security guarantees.

Officials said the fighting started around 1:00 am (2030 GMT Friday), when Taliban militants advanced on the city from several directions.

Gunfire could be heard across Kunduz, the capital of Kunduz province near the Tajik border. As the day wore on, both sides claimed that units from the other's forces were surrendering.

By Saturday evening, the Afghan government said it had gained the upper hand.

The Taliban "wanted to create an atmosphere of fear in the city ... but their attack was repelled by our brave security forces," Ghani said in a statement.

But shortly after that announcement, reports emerged of a suicide attacker targeting the local police chief as he spoke to reporters.

Interior ministry spokesman Nasrat Rahimi said 10 people were killed and the police chief was wounded. It was not immediately clear what had happened and whether any journalists were among the dead.

A few hours earlier, Taliban spokesman Zabihullah Mujahid claimed that several important structures were captured in the attack.

"The Taliban attacked Kunduz city from several directions this morning. We are in the city now capturing government buildings one after the other," he told reporters.

U.S. aircraft supported the Afghan air force in joint air strikes, a U.S. official told AFP, while American trainers gave advice to Afghan ground troops.

Rahimi said "hundreds of Taliban terrorists had been killed", but there was no way to immediately verify the claim.

An AFP journalist in Kunduz said small-arms and heavy-weapons fire could be heard in four areas of the city, but by mid-morning the reports ceased as most area cellphone coverage was cut.

'Peace opportunity'

As for the ninth round of U.S.-Taliban talks in Doha, Western diplomats had widely expected an announcement to have been reached by now, but progress appears to have slowed in recent days.

On Thursday, a U.S. commando was killed in the southern province of Zabul, marking at least the 15th American combat death in Afghanistan this year.

U.S. General Scott Miller, who heads U.S. and NATO forces in Afghanistan, visited Kunduz as Saturday's fighting was ongoing.

Zalmay Khalilzad, the U.S. envoy leading negotiations with the Taliban, wrote on Twitter that he had "raised" the Kunduz attack during talks in Doha, "telling the Taliban that violence like this must stop."

The Taliban attack shows they "don't believe in the peace opportunity provided by the U.S. and the government of Afghanistan", Ghani spokesman Sediq Sediqqi wrote on Twitter.

"On the one hand they are talking with the U.S., on the other hand they are attacking people's houses and villages. We will not leave their attack unanswered."

In late September 2015, the Taliban attacked Kunduz, overwhelming local forces and briefly seizing the city. It was only through extensive U.S. air support that the Taliban were repelled.

The event garnered particular global attention after a U.S. gunship struck a hospital run by Medecins Sans Frontieres (Doctors Without Borders), killing dozens of patients and staff.

The fall of Kunduz also underscored the vulnerability of Afghan security forces and played a role in stopping the pull-out of U.S. forces under president Barack Obama.

Since then the city has come under frequent Taliban attack, but the insurgents have been unable to repeat a full capture.