Karzai also said that Omar could visit Afghanistan "anywhere he wants," but added: "He should put the gun down." Renouncing violence is a condition for Taliban who wish to join government "reintegration" programs intended to draw fighters away from the battlefield.
In inviting Omar to run for office, it was not clear whether the Afghan president was speaking rhetorically - as he once did when, angry at his Western allies, he threatened to join the Taliban.
Omar, the self-styled Commander of the Faithful, has been on the run since the Taliban movement was driven from power in the U.S.-led invasion of 2001. He is believed, like most of the Taliban leadership, to have taken shelter in Pakistan and still has an American bounty on his head.
NATO's International Security Assistance Force declined to comment on Karzai's remarks, saying they were an Afghan government matter. Western officials support starting talks with the Taliban, but say the process has to be "Afghan-led." The Taliban so far has publicly rejected talks with Karzai's government.
The Taliban leadership often derides Karzai as a "puppet," but he has used similar language to describe insurgents who answer to outside groups such as al-Qaeda.
"They are the puppets, working for those who don't want Afghan progress and prosperity," he said.