Mr Khatami's support for the Afghan interim government is important for establishing peace and stability in Afghanistan.
But Mr Khatami's hardline rivals in the Iranian leadership may not approve his unequivocal support for Mr Karzai.
Khatami, a leading reformist, had indicated for weeks he intended to run in the June elections.
CNN: Top Iranian reformer to challenge Ahmadinejad, reports say
Khatami was under pressure from fellow reformists to announce his intentions regarding the upcoming election.
CNN: Top Iranian reformer to challenge Ahmadinejad, reports say
Iran's semi-official Fars News Agency also reported that Khatami formally declared his candidacy on Sunday.
CNN: Top Iranian reformer to challenge Ahmadinejad, reports say
President Muhammad Khatami and his followers run the government and are a majority in parliament.
When President Khatami came to power in 1997, he pledged to tackle the problem.
Mr Khatami, who normally attends the National Students Day ceremonies, stayed away this year.
Mr Mousavi will turn up, as will defeated candidate Mehdi Karroubi and former President Khatami.
Mr Khatami probably agrees but, so far, he has not dared go beyond tentative verbal overtures.
Several European countries, encouraged by Mr Khatami's leanings, have sent trade delegations to Iran.
Mr Khatami has not given up his reform effort, but it appears ever-more timid.
After his election in 1997, Mr Khatami tried to bring Iran closer to the Americans.
Mr Fallahian is the only real hardliner among the nine other candidates competing with Mohammad Khatami.
It is a cruel turnabout of Mr Khatami's pledge to introduce the rule of law.
So Mr Khatami's economic hopes may turn on his ability to carry out political reform.
Mr Khatami's second presidency, if it comes, will be no easier than his first.
Mr Khatami is not a man of confrontation and victory, but of quiet persuasion and unity.
Now Mr Khatami and his supporters are on a roll, able to override crude sniping.
Mr Khatami's predecessor, Ali Akbar Rafsanjani, has positioned himself between the factions, as conciliator.
Mr Khatami has to tread carefully, above all in promoting relations with the West.
Despite tight security, some of Mr Khatami's planned activities have had to be curtailed.
As an incumbent president with a strong mandate, Mr Khatami retains much of his authority.
ECONOMIST: Muhammad Khatami's new cabinet proves disappointing
Mahmud Kashani, a conservative constitutional expert, accuses Mr Khatami of making a bad situation worse.
Mr Khatami's reformers hope that this election will be the start of true party politics.
They favour a free market and less drastic social reform than that advocated by Khatami loyalists.
Mr Khatami, in recent days, has showed no such qualms, appealing for help from all bar Israel.
If Mr Khatami joins the fray, it will not be to elevate Iran but to save it.
On Wednesday, President Muhammad Khatami hinted that the country's co-operativeness might stop if this were to happen.
President Khatami has not yet dared to raise the Rushdie affair, for fear of a conservative backlash.
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