Residents say battle for Sangin district has left them stranded as the clashes continue for the third day.
At least one Afghan civilian was killed and thirteen wounded, after a suicide car bomb exploded close to an entrance to Kabul’s airport, Afghan officials have said.
The attack happened early on Monday morning near the airport’s military entrance, which is used by NATO and coalition forces, the Afghan interior ministry said.
The Taliban claimed responsibility for the attack.
Reporting from Kabul, Al Jazeera’s Abdullah Shahood, said: “We have witnessed an increase in Taliban attacks this year, although it’s winter here and normally Taliban attacks decrease during the winter.
“But we have seen quite a number of attacks by the Taliban, in the south of the country and north of the country, even in Kabul.”
Zia ul Islam, who witnessed the blast, told Al Jazeera that the “explosion was so loud it shook the ground and broke all the windows of the nearby buildings”.
“I am in a state of shock right now. I don’t know how am I even alive. I saw many injured civilians crying for help,” he said.
The attack comes a day after Pakistan’s army chief, General Raheel Sharif, visited Kabul to discuss peace talks with the Taliban.
“Both sides agreed that the first round of dialogue between Afghanistan, Pakistan, US and China will be held in January to lay out a comprehensive roadmap for peace,” the Afghan presidential palace said in a statement.
Earlier this month, a suicide bomber attacked a joint Afghan-NATO convoy near Bagram airbase outside Kabul, killing six US soldiers and wounding three others.
Afghan forces are currently battling to push out Taliban fighters who seized large swaths of the key, opium-rich district of Sangin in southern Helmand province.
US President Barack Obama announced in October that thousands of US troops would remain in Afghanistan after 2016, back-pedalling on previous plans to shrink the force and acknowledging that Afghan forces were not ready to stand alone.