The militant Islamist group claimed responsibility and its reclusive leader, Mullah Mohammad Omar, urged Afghans to wage jihad to establish a Islamic rule in Afghanistan, calling the election a "publicity stunt".
"You would have, by now, come around to know what sort of unqualified figures, being loyal to foreigners' interests, have been imposed on you by the Americans," the Taliban's one-eyed leader said in his yearly Eid Al-Adha message.
President Ashraf Ghani was inaugurated on Monday after months of deadlock over who won the election that threatened to rekindle outbreaks of violence along ethnic lines.
Under the terms of a U.S.-brokered deal ending the stand-off, the new president and his former rival, Abdullah Abdullah, will share power.
During Ghani's first three days of rule, he has signed long-delayed security deals with NATO and the United States allowing troops to stay beyond 2014.
Seven people were killed when the international airport was attacked on Monday, while two bombs detonating in the east and west of the city on Wednesday killed at least seven people.
The Taliban claimed responsibility for the earlier attacks, vowing to fight the new "stooge regime".
© Thomson Reuters 2014