Hopes for an end to Afghanistan's decades of war were raised in late February when the Taliban and the United States struck a deal on the withdrawal of U.S.-led foreign forces in exchange for Taliban security guarantees.
But the deal did not include a ceasefire, which has been left to the U.S.-backed government to negotiate with the insurgents.
A Taliban spokesman, Suhail Shaheen, said in a post on Twitter that a ceasefire would be possible if the peace process was being implemented "fully" but "hurdles" meant the Taliban would not yet lay down their arms.
"Asking for ceasefire is not rational and convincing," Shaheen said in his post late on Thursday.
President Ashraf Ghani called on Thursday for the ceasefire for Ramadan, which began in Afghanistan on Friday, and to allow the country to focus on what he said was a critical novel coronavirus outbreak spreading all over the country.
Afghanistan has detected more than 1,300 cases of the virus but health experts say the number could be higher as testing is limited and Afghanistan's weak health system would struggle with a widespread outbreak.
The Taliban, fighting for years to expel foreign forces, agreed in February to a week-long "reduction in violence" to secure the agreement with the United States, which was signed on Feb. 29. But they resumed attacking government forces soon after.
This week alone, dozens of members of the Afghan security forces, civilians and Taliban fighters have been killed in clashes.
In one of the latest incidents, Taliban forces attacked security checkpoints manned by members of a pro-government militia in the northwestern province of Badghis late on Thursday.
Thirteen members of the militia were killed and seven captured, said Najmuddin Burhani, spokesman for the provincial governor.