Afghan officials say a nearly day-long Taliban assault on Kabul has ended after security forces killed the remaining insurgents.

The Afghan interior ministry made the announcement Wednesday, some 20 hours after militants first launched their coordinated assault on several high-profile targets in the capital.

On Tuesday, insurgents armed with suicide vests and rocket-propelled grenades targeted NATO's headquarters, the U.S. Embassy, the Afghan Intelligence Agency and other areas, killing at least seven people.

As part of the assault, six militants stormed a multi-floor building under construction on the edge of Kabul's diplomatic district, which provided them clear shots on the nearby U.S. Embassy and NATO headquarters. There also was a simultaneous series of explosions around the surrounding neighborhood.

By nightfall Tuesday, NATO helicopters were circling over the high-rise construction site as Afghan security forces moved through the building in an attempt to subdue the one or two insurgents believed to be remaining from the assault.

Both NATO and the U.S. Embassy said none of their staff were wounded in the attack.

In Washington, CIA director David Petraeus told U.S. lawmakers that a rocket-propelled grenade hit the U.S. Embassy complex, wounding four Afghans who were lined up to wait for American visas.

Afghan President Hamid Karzai condemned the attack and praised the effective response of the Afghan authorities. He said such actions will not stop the security transition in the country, but instead embolden the Afghan people's determination to take responsibility for their own country's affairs.

The assault came as NATO nations seek to transfer full security control to the Afghan military within the next few years. U.S. and NATO officials responded to the violence by saying it would not deter their resolve in continuing the transition through the end of 2014. Afghan security forces already have taken security control of several cities and provinces.