However, he said he expected the United States to apologize to Iranians before diplomatic relations could be restored.
Iran and Washington severed ties in 1979 when 52 Americans were kidnapped and held in the U.S. embassy in Tehran for over a year. Relations came under further pressure in the last decade over Iran`s nuclear ambitions.
Under the agreement reached in July, Iran is to curb its nuclear program in exchange for an easing of sanctions on its economy. Tehran denied Western suspicions it wanted to develop an atomic bomb.
"The way this agreement is applied can have an impact on the future," Rouhani said in an interview with Italy`s Corriere della Sera newspaper ahead of his trip to Italy this weekend, his first to a European capital.
"If it is well applied it can lay the foundation for fewer tensions with the United States, creating the conditions to open a new era. But if the Americans don`t respect their part of the nuclear accord, then surely our relationship will remain as it has been in the past," he said.
The United States approved conditional sanctions waivers for Iran, though it has cautioned they would not take effect until Tehran has complied with the nuclear accord.
Asked about the possible re-opening of embassies, Rouhani said: "One day these embassies will re-open but what counts is behavior. The Americans hold the key to this."
He added that if "they modify their policies, correct errors committed in these 37 years and apologize to the Iranian people, the situation will change and good things can happen".
The moderate Rouhani came to power in 2013 promising reforms, but critics have accused him of making little headway. But the president defended his record, saying he faced constraints.
"The executive by itself cannot resolve everything. There must be cooperation with the judicial and legislative system. We hope it will happen in the future."
Rouhani is due to see the Italian prime minister and business leaders during his Nov. 14-15 visit to Rome and will also hold talks with Pope Francis.
The Iranian president will fly to France for talks in Paris on Nov. 16-17.
Rouhani says U.S.-Iran ties could be restored but U.S. must apologize
12 November 2015
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The nuclear deal between world powers and Iran could lead to better relations between Tehran and Washington and the eventual re-opening of embassies in both capitals, Iranian President Hassan Rouhani was quoted as saying on Thursday.
