Suspected Taliban fighters fired a rocket into a hospital in Afghanistan on Wednesday, sparking a blaze that caused extensive damage and destroyed Covid-19 vaccines though there were no reports of casualties, government officials said.

In northern Afghanistan, the Taliban captured the town of Shir Khan Bandar, a dry port on the border with Tajikistan, sending customs workers and members of the security forces fleeing to safety over the border.

Fighting between government forces and the insurgents has surged in recent weeks, with the militants gaining control of more territory as the last US-led international forces prepare to leave after two decades of fighting.

Taliban spokesman Zabihullah Mujahid denied responsibility for the attack on the hospital in the eastern province of Kunar, which a provincial health director said resulted in the loss of crucial supplies.

"Different types of vaccine, including doses meant to fight polio and Covid-19 were destroyed in the fire," said Kunar health official Aziz Safai.

Afghanistan has reported 4,366 deaths due to Covid-19 infections and 107,957 cases, as of Wednesday.

Many health officials say the real number of coronavirus infections is likely much higher but many cases are not being detected because of little testing.

The virus has been spreading as insecurity has been growing, especially since May 1 when the United States began the final stages of its troop withdrawal and the Taliban stepped up attacks on government forces.

Tajikistan's border guard service said in a statement late on Tuesday that it had allowed 134 Afghan servicemen to retreat into Tajikistan from Shir Khan Bandar, about 50 kilometres from the city of Kunduz.

The Taliban seized ammunition and armoured vehicles in the town after Afghan authorities surrendered it to the advancing insurgents, Afghan officials said.

The loss of the trading town will be a blow to the US-backed government as it struggles to stop Taliban advances in different parts of the country.

In a statement on Wednesday, the Taliban said border trade ports that have fallen under the control of their fighters shall continue to operate.

"All commercial import and export will function as normal and administrative work of traders will continue uninterrupted," the militant group also invited Afghan security forces and those working for the democratically elected government to "embrace the open arms of the Islamic Emirate (Taliban rule)".

"We shall welcome and honor them, and send them to their homes and families with complete assurance."

The group also instructed its fighters to ensure the security of public spaces, businesses and civilian residences is not harmed in the ongoing clashes.