Security is tightened around the capital. Till now there were not reports of casualties.
Taliban spokesman Zabiullah Mujahid, said that their fighters had fired four rockets at the airport. He said the power of the airport was cut as the rockets triggered heavy explosions.
The delegates include representatives from 57 countries and 11 regional and international organizations.
Nearly 70 international representatives are to participate in the Kabul Conference, which will support new development projects and transfer more aid money and responsibility to the Afghan administration.
In Jun, the Taliban tried to attack a peace conference in Kabul where tribal elders and lawmakers gathered to discuss a deal with the militants.