KABUL, April 7 (Reuters) - The Taliban killed at least seven Afghans in an attack on an aid convoy in the southwest of the country on Saturday, police said, as fighting intensifies after the bloodiest year since the militants were ousted in 2001.

Attackers fired rocket-propelled grenades at the convoy, killing six. The seventh was a local woman killed in her home in the area in Farah province. No further details were available.

More than 4,000 people, 1,000 of them civilians, died in fighting last year in what NATO and the United States have called heavier than expected resistance by a resurgent Taliban, bolstered by record drug crops and shelter in Pakistan.

About 5,000 NATO and Afghan troops have launched a major offensive in neighbouring Helmand province, the opium heartland of the world's biggest producer.

President Hamid Karzai, facing his own new and unexpected political challenge, on Friday said for the first time he had spoken to Taliban leaders in a bid to end the fighting.

Those comments came hours after a suicide bomber killed at least six people near the country's parliament in Kabul, the latest in a series of increasing attacks in the city.

Karzai, whose rule critics and many analysts consider weak and ineffective, repeated offers on Friday that all Afghans, including fugitive Taliban leader Mullah Mohammad Omar, were welcome for talks to end ever-bloodier fighting.

The United States and some of Karzai's advisers had said such offers were conditional.

Leading lawmakers, cabinet members and government advisers formed a new group, the National Front, this week to challenge Karzai amid mounting dissatisfaction with his rule.

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