The blast went off near a tent where more than 1,000 people had congregated in Tani district of Khost province at the funeral for Gov. Abdul Hakim Taniwal, who died with two others in a suicide attack outside his office in neighboring Paktia province on Sunday.
Mohammed Ayub, the provincial police chief, said at least five police were killed. The attacker also died.
In other developments:
Ayub said four federal ministers — for interior, refugees, telecommunications and administrative affairs — had attended but were unhurt. They were about to leave by helicopter when the bomb went off. They had been about 800 yards away from the explosion, he said.
Police established two security cordons around the ministers who flew out soon after, he said.
Between 30 and 40 wounded and two dead policemen had been brought to the hospital in the Khost provincial capital, about 30 miles to the north of Tani, Dr. Alam Gul said.
An AP Television News cameraman at the scene said police fired warning shots in the air as the crowd panicked after the blast and rushed to escape, amid fears there might be a second bombing.
Sunday's attacker, with explosives attached to his body, ran toward Taniwal's car as he left the office and detonated a bomb. The governor's nephew and a bodyguard also died. Three police were wounded.
Mohammed Hanif, who claims to speak for the Taliban, claimed responsibility for that attack and threatened more.
Taniwal is the highest-profile of victim in a series of suicide attacks launched by supporters of the former ruling Islamic regime this year.
He had been governor of Paktia for about a year and a half. Before that, he was federal minister of mines and industry in the Cabinet of President Hamid Karzai.
Boucher said the increase in fighting by the Taliban was the result of efforts to extend the Western-backed President Hamid Karzai's shaky control to the lawless southern regions.
"This is a dangerous period, a difficult period. But it's a necessary one in order to establish the authority of the government throughout the nation," Boucher said, repeating an explanation offered by other U.S. officials for the surging violence in Afghanistan over the past three summers.
Five years after the Sept. 11 attacks that triggered the U.S.-led invasion of Afghanistan, Boucher said the country's massive opium industry, criminal groups and ineffective local governments were also to blame for the instability.
Reconstruction projects, Pakistani efforts to rein in militants on its side of the border and a stiffened counter-narcotics program would eventually help turn the tide, he said.
"The basis process under way is a positive one," Boucher said.
NATO commanders planned to meet in Brussels this week to discuss the issue of reinforcements. They have called for reinforcements for British, Canadian and Dutch troops engaged in battling militants in Kandahar and Helmand provinces.