At least 42 people were wounded.
The attack - which came on the heels of a major upsurge in rebel violence in recent months including assassinations, near-daily clashes with rebels and the kidnapping of an Italian aid worker - further raised fears that militants here were copying the tactics of insurgents in Iraq.
Many local leaders had been expected to attend the funeral of Mullah Abdul Fayaz, the top Muslim leader in the province, whom the mosque is named after.
Fayaz, a supporter of U.S.-backed President Hamid Karzai, was gunned down in Kandahar on Sunday by suspected Taliban gunmen - a week after he led a call for people not to support the militant group.
Kandahar Gov. Gul Agha Sherzai said the suicide bomber's body had been found, and that he was part of Osama bin Laden's terror network.
"The attacker was a member of al-Qaida. We have found documents on his body that show he was an Arab," Sherzai told reporters.
Kandahar was a stronghold of the hard-line Taliban regime that was ousted from power in late 2001 by U.S.-led forces for harbouring bin Laden.
The British Broadcasting Corp. reported that it received a call from a man claiming to be a Taliban member who said the movement was responsible for the attack. It did not identify the caller or say if the report had been verified.
Hundreds of mourners were crowded inside the Mullah Abdul Fayaz Mosque in Kandahar, the main southern city, when the bomb exploded at about 9 a.m. local time, leaving blood and body parts over a wide area.
Interior Ministry spokesman Latfullah Mashal said the capital's police commander, Gen. Akram Khakrezwal, was killed along with other police officers attending the funeral. Mashal said it was a suicide bombing.
Kandahar's deputy police chief, Gen. Salim Khan, said the explosion occurred near where people remove their shoes before praying.
Nazir Ahmadzai, a doctor at Kandahar Hospital, said 20 people were killed and 45 wounded - many of them Khakrezwal's bodyguards. The hospital's director, however, said 72 people were wounded, four gravely.
Mashal, the Interior Ministry spokesman, denounced the attack as an atrocity against both the nation and Islam.
"They are the enemies of peace and the enemies of Islam," he said. "Attacking Muslims while they are offering prayers and performing religious ceremonies is completely against Islam, against our country."
Col. James Yonts, the U.S. military spokesman in Afghanistan, said the attack was an "atrocious act of violence upon innocent civilians and a mosque."
Even before the blast, security was tight. Afterward, more police were deployed around the mosque, the main city hospital and other sites around the city.
In a second attack Wednesday, a bomb exploded on a bridge west of Kandahar as a group of Afghan de-miners were driving over it, killing two and wounding five, said Patrick Fruchet, spokesman for the UN Mine Action Centre for Afghanistan.
The seven were working on a project funded by the Japanese government, he said.
Kandahar has been targeted by bombs in the past.
On March 17, a roadside blast killed five people and wounded more than 30. Authorities blamed anti-government rebels for the attack, which took place as U.S. State Secretary Condoleezza Rice was in the capital, Kabul, about 450 kilometres to the north.
In January 2004, a bomb attached to a bicycle killed at least 15 people, most of them children, and injured dozens more in the city. Authorities blamed Taliban militants.
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