At least nine rockets hit near the diplomatic area of the Afghan capital, Kabul, where President Ashraf Ghani was delivering a speech to mark the beginning of the Eid al-Adha holiday.
Afghan officials on Tuesday said fighting broke out between security forces and armed groups in the city's old quarter, in which at least two people were wounded.
"This morning a group of terrorists took over a building in Reka Khana and fired several rockets towards Kabul," Najib Danishm a spokesman for the interior ministry told AFP news agency.
The attack comes as the Taliban rejected a ceasefire offer from the Afghan government on Monday, saying they would persist with their attacks.
Earlier on Monday, Taliban fighters ambushed three buses carrying nearly 200 passengers travelling for Eid.
Reuters news agency reported that 160 of them were later released, while at least 20 remain captive.
Two Taliban commanders said their supreme leader rejected Ghani's Sunday offer of a three-month ceasefire, beginning with this week's Eid, Reuters reported.
In June, the Taliban observed a government ceasefire over the three-day Eid al-Fitr festival, leading to unprecedented scenes of government soldiers and Taliban fighters embracing on front lines, and raising hopes for talks.
But one of the Taliban commanders said the June ceasefire had helped US forces, who the Taliban are trying to drive out of the country.
Taliban leader Mullah Haibatullah Akhunzada rejected the new offer on the grounds that it too would only help the American-led mission.
