Hundreds of commandos were deployed to the western city of Herat while authorities in the southern city of Lashkar Gah called for more troops to rein in the assaults.
Fighting has surged across the country in the months 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 key border crossings, the Taliban have started to besiege provincial capitals.
Flights out of Kandahar, Afghanistan's second-largest city and was also the former bastion of the group, were halted after rockets struck the airport before dawn.
Airport chief Massoud Pashtun said two rockets had hit the runway and repairs were underway with planes likely to resume service later on Sunday.
The facility is vital to maintaining the logistical and air support needed to keep the Taliban from overrunning the city, while also providing aerial cover for large tracts of southern Afghanistan.
The attack came 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 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, a city of 200,000 residents.
"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 city's outskirts overnight with air strikes targeting Taliban positions.
Herat provincial governor's spokesman Jailani Farhad said that around 100 militant fighters had been killed in the attacks.
Both the Taliban and government forces tend to exaggerate their claims of casualties inflicted on each other's forces and true counts are difficult to independently verify.
On Sunday, the Ministry of Defense said that hundreds of commandos had been sent to Herat to help beat back the insurgent assault.
"These forces will increase offensive operations and suppress the Taliban in Herat," the ministry tweeted.