In remarks before the United Nations General Assembly on Tuesday, Obama pushed for a "diplomatic path" with the new Iranian government.
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"I don't believe this difficult history can be overcome overnight - the suspicion runs too deep," Obama said in his speech.
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"But I do believe that if we can resolve the issue of Iran's nuclear program, that can serve as a major step down a long road towards a different relationship - one based on mutual interests and mutual respect."
The moderate Donya-e-Eqtesad daily greeted his 'different tone', while the conservative Jomhouri Eslami reveled in a declaration that "the United States does not seek regime change" in Iran.
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.
"Even those most pessimistic to an opening in relations have accepted that the time for change has arrived," the paper's editorial said.
Engaging in negotiations with Washington over Iran's nuclear drive, Shargh said, would culminate in the recognition of Iran's "rights."
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, reveled in Obama's declaration in recognizing 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 program was "a sign of Iran's power."
Political analyst Saeed Leylaz, writing in Shargh, was critical of "the illusion of a magic wand" that possible rapprochement with the United States would solve all of Iran's problems.
"Negotiations cannot solve the economic and political problems of Iran," he said. "The solution must come from within."
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