The explosion destroyed the two embassy vehicles, blew the embassy gates off, all-but demolished the embassy walls and badly damaged buildings inside the compound. Windows were shattered hundreds of metres (yards) away.
Forty-one people were killed and 139 wounded, a senior police official said.
"The Interior Ministry believes this attack was carried out in coordination and consultation with an active intelligence service in the region," the Afghan Interior Ministry said.
The militants have vowed to step up their campaign of suicide bombings this year, graphically demonstrating that despite the increase in foreign troops in Afghanistan and more trained Afghan forces on patrol, the Taliban are far from being a spent force.
"With this cowardly attack, the enemies of peace in Afghanistan wanted to hurt ongoing friendly relations of Afghanistan with the rest of the world, especially India," Karzai said in a statement. "Such attacks will not hamper Afghanistan's relations with other nations." India has close relations with the Afghan government and is funding a number of large infrastructure projects.
"The government of India strongly condemns this cowardly terrorist attack on its diplomatic mission in Afghanistan. Such acts of terror will not deter us from fulfilling our commitments to the government and people of Afghanistan," the Indian Foreign Ministry said in a statement.
India's rival Pakistan was the main backer of the Taliban when they ruled Afghanistan from 1996 to 2001, but Islamabad officially dropped support for the austere Islamist movement as a result of intense U.S. pressure in the wake of the September 11, 2001 attacks, ordered by al Qaeda leaders hosted by the Taliban.
In the Pakistani capital Islamabad, police allowed up to 70 Kashmiri activists to enter the diplomatic enclave where they chanted anti-India slogans outside the Indian High Commission.
An Indian diplomat said their appearance caused some alarm because the Pakistani authorities would normally forewarn the embassy of any demonstration, but no warning was given this time.
