(Updates with Taliban claim of responsibility)

KABUL, April 6 (Reuters) - A suicide bomber killed six Afghans, including a policeman, in a blast near the country's parliament in Kabul on Friday, President Hamid Karzai said.

The Taliban claimed responsibility for the attack in a satellite phone call to Reuters and vowed to stage more.

Police had stopped the bomber in his car and then he blew himself up, a policeman at the scene said.

Police earlier said four people, including the police officer who spotted the bomber and three civilians, were killed. But Karzai, who addressed a news conference later in the day, said the death toll was six.

"Six of our countrymen were martyred in this incident," he told reporters at his heavily fortified presidential palace.

Pieces of flesh littered the road and a large crowd gathered at the site of the attack.

The blast occurred early in the morning and there was little traffic because Kabul largely shuts down on Fridays, the Muslim holy day.

There has been a series of suicide blasts in the capital as the country heads into renewed fighting between Taliban and Western troops after the annual winter lull.

Last year was the bloodiest since the Taliban were ousted in 2001 -- more than 4,000 people died -- and many military commanders and analysts expect fighting this year to be worse.

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