At least two rockets exploded at 5:00 am (0030 GMT), the exact time that the insurgents had vowed to start a new nationwide operation against US-led foreign forces and Afghan government facilities.
Taliban leaders said last week that the offensive, which will be the last before NATO combat troops withdraw from Afghanistan, would cleanse "the filth of the infidels" from the country.
"Two rockets landed north of Kabul international airport," Sediq Sediqqi, the interior ministry spokesman, told AFP. "There were no casualties."
It also said that mortars have been fired at Bagram airport, the biggest ISAF base in Afghanistan, which lies north of Kabul.
The Taliban claimed responsibility for the attacks via a recognised Twitter account, and said other strikes had been carried out across the country.
The "Khaibar" offensive, named after an ancient battle between Muslims and Jews, will coincide with a second round of elections next month to choose a successor to President Hamid Karzai, who has ruled since the fall of the Taliban in 2001.
A small number of US troops may stay on from next year on a training and counter-terrorism mission, but the Taliban warned that the insurgency would continue against even a few thousand US troops.
The Taliban "insists on the unconditional withdrawal of all invading forces," the group said in an English-language statement on its website last week.
The statement said that attacks during the coming "fighting season" would target US military bases, foreign embassies and vehicle convoys, as well as Afghan officials, politicians and translators.
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