Iran's news agency says Hekmatyar has left Tehran
The official Iranian news agency IRNA said Gulbuddin Hekmatyar had left his home in exile in the Iranian capital Tehran for an unknown destination after the government ordered him out of the country.
The past month has seen a war of words between the US and Iran - accused by President George W Bush of being part of an "axis of evil" and of trying to destabilise the newly-established Afghan administration.
The report on IRNA came soon after Mr Karzai left Iran on Tuesday after a three-day visit during which the two neighbouring countries pledged to co-operate to bring stability to the region.
Expulsion order
"A few days ago a decision on the necessity of Hekmatyar's leaving Iran was delivered to him," IRNA quoted an Iranian source as saying.
"Afterwards Hekmatyar left his residence to an unknown destination and it is still unclear where he has gone and where he is living now," the source said.
Mr Hekmatyar, a former anti-Soviet mujahideen commander, fled to Iran in 1996 when the Taleban took control of Kabul.
It was unclear where he would be able to go.
War crimes allegations
An Afghan Foreign Ministry spokesman told the Reuters news agency on Monday that Hekmatyar would be arrested and tried for war crimes if he returned home.
Pakistan, once Mr Hekmatyar's main backer in the fight against the Soviet occupation of Afghanistan but later allied with his Taleban opponents, is also considered unlikely to take him back.
Analysts say Iraq could be a possible destination.
Iran closed the offices of Mr Hekmatyar's Hezb-i Islami (Islamic Party) earlier this year after the former warlord said he was opposed to Afghanistan's interim government and had organised forces in Afghanistan to fight foreign troops there.
Despite Iranian declarations of support for the interim Afghan administration, Washington has accused Tehran of sending arms into Afghanistan and allowing Taleban and al-Qaeda members to escape across the Iran-Afghan border.