Rockets landed at a time when President Ashraf Ghani was speaking during at an Eid prayer ceremony, two days after he declared a "conditional ceasefire" with the Taliban.
The Taliban rejected on Monday an Afghan government offer of a ceasefire and it would persist with their attacks, two militant commanders said, while insurgents ambushed three buses and kidnapped almost 200 passengers travelling for a holiday.
Insurgent commanders told Reuters the leadership believed any truce would only lengthen the U.S. mission to back up Mr Ghani's government.More news: Madonna Gives Aretha Franklin a Baffling Tribute at the 2018 VMAs
"Our leadership feels that they'll prolong their stay in Afghanistan if we announced a ceasefire now", a senior Taliban commander, who declined to be identified, said by telephone.
The Foreign Office spokesperson, in a statement, urged all parties to respond to the government's ceasefire offer.
Earlier this month, the insurgents launched a coordinated assault on Ghazni, a strategic city only 120 kilometers (75 miles) from the capital, Kabul.More news: Battlefield V Beta Starts September 4
A Kabul police chief told the BBC that three attackers armed with a heavy machine gun and a mortar had broken into a building behind Kabul's Id Gah Mosque. The outlet said, citing officials, that at least 12 missiles exploded in the area, adding that locals say there might have been more than 20.
Kunduz provincial council member Sayed Assadullah Sadat said people on the buses were travelling to be with family in Kabul for the holiday. The Defense Ministry said about 200 militants were killed.
Ghani unveiled the government's latest ceasefire gambit during an Independence Day address late on Sunday, saying security forces would observe the truce beginning this week - but only if the militants reciprocated.More news: Cricket WATCH: Virat Kohli celebrates his century with a Flying Kiss