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By Victoria Cavaliere

NEW YORK, Nov 24 (Reuters) - Prominent Iranian-Americans praised the Iranian nuclear deal as a significant first step in what they hope will be a broader rapprochement between Iran and the international community.

While the deal will give a psychological boost to many Iranians and provide momentum to moderate Iranian President Hassan Rouhani, some Iranian-Americans cautioned, improvements in the country's economy and in its treatment of dissidents will not occur overnight.

The agreement reached early Sunday has at least the potential to become a milestone, said Reza Aslan, an Iranian-born scholar of religion and author of the book "Zealot."

"I don't think these negotiations are going to have an effect either on Iran's global image or on Americans' perceptions of Iran," he said. "But they may set the groundwork for eventual normalization between Iran and the U.S. - and that is something which should be celebrated."

Aslan said virtually every Iranian outside the country's political, military or religious elite has suffered from the economic sanctions.

The sanctions, first imposed in 2006 by the United Nations over the country's nuclear program, along with trade restrictions between the United States and Iran in place since 1979, have slashed Iran's oil sales and largely frozen it out of the global banking system.

San Francisco Sheriff Ross Mirkarimi, born in the United States to an Iranian father and a Jewish mother, described the deal as a positive step.

"For anybody who has had direct and intimate contact with people living in Iran, the first sign of relief will be about the economics," said Mirkarimi, who has friends and extended family in Iran. "I know that's on many people's minds. They don't like to see their loved ones harmed."

Omid Memarian, an Iranian journalist and blogger persecuted in his home country before coming to the United States in 2005, said the deal will give hope - if not immediate help - to members of his family in Tehran who have struggled to make ends meet.

Memarian said his brother's Tehran-based food-import business has floundered largely as a result of Iran's depressed currency, the rial, which jumped more than 3 percent against the U.S. dollar on Sunday after the deal was announced.

Memarian warned, however, that the nuclear deal does not mean Iran will ease its hard line on those in the country who speak out against the regime, and said his own return would be fraught with risk.

"People are now questioning Rouhani's determination to uphold the people's rights," Memarian said. "That's going to be one of his major challenges in the months to come - whether he stands up for his people or gives up the domestic issues to the hard-liners in Tehran."