President Hamid Karzai, who has been the only leader in Afghanistan since the 2001 US-led invasion brought down the Taliban, will not seek a third term in office, his palace said Thursday.

"The constitution of Afghanistan does not allow anyone to run for the presidency for more than two terms," the statement quoted Karzai as telling a group of parliamentarians.

He "will not try to run for the presidency for the third time", it added.

Karzai was sworn in as interim leader of Afghanistan in December 2001, shortly after the US-led invasion toppled the Taliban.

In 2004, he won the country's first direct presidential elections with 55.4 percent of the vote.

But his re-election in 2009 was mired in allegations of corruption, in which challenger Abdullah Abdullah abandoned a second-round run-off and investigators threw out a third of Karzai?s original votes because of fraud.

Thursday's announcement comes the day after Karzai handed authority for resolving a long-running row over vote-rigging in last September's parliamentary elections to the Independent Election Commission.