Afghan government forces struggled against Taliban assaults on several major cities on Sunday, as a crucial airport in the south came under rocket fire overnight.
Fighting has increased since early May, when US-led foreign forces began a final withdrawal from Afghanistan that is now almost complete.
After seizing large tracts of rural territory and capturing border crossings, the Taliban have now started to besiege provincial capitals.
Flights out of Kandahar, Afghanistan's second-largest city, were halted after rockets struck the airport before dawn.
“Kandahar Airport was targeted by us because the enemy were using it as a centre to conduct air strikes against us,” Zabiullah Mujahid, a Taliban spokesman, told Reuters.
Afghan government officials said the rocket attacks forced authorities to suspend all flights and that the runway was partially damaged. There were no immediate reports of casualties, the officials said.
But within the city on Sunday, a mortar shell struck a taxi, killing at least five civilians including two children, an Afghan official said.
Kandahar airport is vital to providing the logistical and air support needed to keep the Taliban from overrunning the city, while also providing aerial cover for large parts of southern Afghanistan.
The attack happened as the Taliban inched closer to overrunning at least two other provincial capitals, including nearby Lashkar Gah in Helmand province.
“Fighting is going on inside the city and we have asked for special forces to be deployed in the city,” Ataullah Afghan, head of the Helmand provincial council, told AFP.
Afghan security forces have increasingly relied on air strikes to push the militants back from cities even as they run the risk of hitting civilians in heavily populated areas.
“The city is in the worst condition. I do not know what will happen,” said Halim Karimi, a resident of Lashkar Gah.
“Neither the Taliban will have mercy on us, nor will the government will stop bombing.”
Further west, in the city of Herat, fighting continued on the outskirts overnight with air strikes on Taliban positions.
The Herat provincial governor's spokesman Jailani Farhad said that about 100 Taliban fighters had been killed in the attacks. Late on Sunday afternoon, the Afghan government appeared to have deployed commandos to Herat ahead of an expected Taliban assault.
Both the Taliban and government forces exaggerate their claims of casualties inflicted on each other's forces and true counts are difficult to independently verify.
For months, the Taliban's territorial gains during the final stages of the US military withdrawal have largely been in sparsely populated rural areas.
But in recent weeks they have brought increasing pressure on provincial capitals and seized key border crossings.
The capture of any major urban centre would take their current offensive to another level and fuel concerns that the army is incapable of resisting the Taliban's battlefield advances.
The government has repeatedly dismissed the Taliban's steady gains over the summer as lacking strategic value.
In recent weeks, the Afghan government's air force has provided Kabul with its biggest battlefield advantage over the Taliban and has so far largely kept the insurgents from overrunning urban areas.