In remarks before the United Nations General Assembly yesterday, Obama pushed for a "diplomatic path" with the new Iranian government.
"I don't believe this difficult history can be overcome overnight -- the suspicion runs too deep," Obama said in his speech.
"But I do believe that if we can resolve the issue of Iran's nuclear programme, that can serve as a major step down a long road towards a different relationship -- one based on mutual interests and mutual respect."
The reformist Shargh newspaper hailed the US leader's speech for opening up "a new path" for the relationship between the two arch-foes, which have had no diplomatic ties since 1980.
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"Even those most pessimistic to an opening in relations have accepted that the time for change has arrived," the paper's editorial said.
It added that the international situation has "significantly changed in Iran's favour", and argued that Israeli Prime Minister Benjamin Netanyahu would be "isolated" as a "warmonger".
Another reformist daily, Etemad, quoting former deputy foreign minister Mehdi Mohtashami, said Obama acknowledging "past mistakes" was a sign that the two sides "have the will to fight against mistrust".
Several newspapers, including the government-run Iran daily, revelled in Obama's declaration in recognising a religious decree by supreme leader Ayatollah Ali Khamenei on a ban against weapons of mass destruction, including nuclear arms.
Optimism was not shared by all the Islamic republic's media, however.
The hardline Kayhan daily mocked Obama's "jabbering against Iran", while saying his declared respect for Tehran to operate a peaceful nuclear programme was "a sign of Iran's power".