Taliban fighters have seized a military hilltop site in Kunduz, tightening their grip on the northern Afghan city.
The capture of the Bala Hisar fortress came despite efforts by government reinforcements, backed by Nato airstrikes and special forces, to retake the city.
It leaves the airport as the army’s last stronghold.
The Taliban overran Kunduz on Monday, their biggest military gain since they lost power in 2001.
The Taliban had blockaded the Bala Hisar fortress for two days.
The nearly 200 Afghan security personnel then abandoned the position after running out of food and ammunition, an Afghan security official told Reuters.
Late on Tuesday the Taliban tried to capture the airport as well, but US air strikes and coalition special forces halted their advance. A special forces commander said the foreign troops – who are in Kunduz in a non-combat role – had acted in “self-defence”.
Clashes went on through the night around Kunduz, and the provincial hospital was reportedly struggling to cope with the number of casualties.
Afghanistan’s health ministry said more than 40 people had been killed and more than 330 injured in the fighting, the vast majority of them civilians.
Kunduz is one of Afghanistan’s largest cities, and is strategically important as a transport hub for the north of the country.
Militant violence has increased across Afghanistan since Nato ended its combat mission in Afghanistan in December, leaving a 13,000-strong residual force used for training and counter-terrorism operations.
The BBC’s Dawood Azami says the Taliban are now trying to open multiple fronts to divert the attention of the Afghan military from Kunduz and stretch them thin.
On Tuesday the United States acknowledged the seizure of Kunduz as a setback, but said it remained confident that Afghan security forces could retake the city.
Sayed Sarwar Hussaini, a spokesman for Kunduz’s police chief, told Reuters: “Hundreds of Taliban are killed and their dead bodies are on [the] streets.”
There was no independent confirmation, and the Taliban denied their local leader had been killed.
The Afghan defence ministry claimed on Tuesday that the town’s police headquarters and prison had been recaptured, after militants released hundreds of prisoners when they took the city on Monday.
But Taliban-released video featured militants in the town showing off seized tanks, armoured vehicles, police cars and Red Cross vans.
