But Mr Khatami's hardline rivals in the Iranian leadership may not approve his unequivocal support for Mr Karzai.
Mr Karzai has cancelled a scheduled press conference with visiting US Defence Secretary Chuck Hagel.
BBC: Hamid Karzai says US and Taliban sowing post-2014 fears
In recent weeks Mr Karzai has created unwanted turmoil, for the second year running.
Meanwhile relations between Mr Karzai and his international backers have dipped to yet another new low.
During the speech, Mr Obama outlined the agreement he had just signed with Mr Karzai.
BBC: Barack Obama pledges to 'finish the job' in Afghanistan
Mr Karzai also warned that there were also increasing signs of a stronger warlord culture.
Mr Karzai has now called for NATO-led forces to keep out of Afghan villages.
Nobody is taking to the streets to demand that Mr Karzai welcome the Taliban back.
Mr Karzai said he had been told the air strike was requested by Afghan forces.
Mr Karzai and Mr Obama committed to crafting a bilateral security agreement as soon as possible.
BBC: US troops will end 'most' Afghanistan combat this spring
Mr Karzai's supposedly corrupt half-brother was meant to go, but he remains in charge in Kandahar.
There are a number of explanations for Mr Karzai's outbursts, other than the psychotropic or psychotic.
Mr Karzai depends on international support for his survival, so is he going completely mad?
Mr Karzai had ordered a ceasefire, but rivalry between the two groups is huge.
Mr Karzai's trip to Washington comes at a crucial time for relations between the two countries.
Strangely, given Mr Karzai's declining popularity, few prominent rivals have yet announced their intention to run.
In the meantime, Mr Karzai has repeatedly asked for the ISAF to be expanded beyond Kabul.
Mr Karzai's own clout will continue to depend on the presence of international troops.
If Mr Karzai's recent cabinet reshuffle heralds more resolute action, he could yet redeem himself.
Mr Karzai said Afghanistan would "definitely be able to provide for the security of the Afghan people".
Talks in Bonn between four Afghan factions agreed on an interim government which Mr Karzai would lead.
ECONOMIST: An outline for power-sharing that may just work. Maybe
Mr Karzai is too often keen to distance himself from foreign allies while counting on their support.
ECONOMIST: Singular incident or harbinger of something worse?
Mr Karzai seems to have stopped lambasting Pakistan for tolerating sanctuaries within its borders for Taliban insurgents.
Mr Karzai is from the Pushtun ethnic group, the country's largest, which has traditionally ruled the country.
Mr Karzai said if Osama Bin Laden were caught he would be handed over to international justice.
Mr Karzai is often criticised by the Taliban for being a puppet of Western governments, our correspondent says.
BBC: Karzai speech 'put Nato forces at risk', commander warns
Acknowledging his victory this week, Mr Karzai predicted that naming his ministers would be like opening Pandora's box.
ECONOMIST: Hamid Karzai must now put his electoral victory to good use
Mr Karzai barely escaped an attempt on his life in the former Taliban stronghold of Kandahar last year.
Regarding former members of the Taleban, Mr Karzai said those who had no criminal record would be freed.
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