Iranians say they're hoping it means a new era for their country and an end to crippling economic sanctions.
Iran's new president has pushed for better relations with Washington and tweeted happy new year to the world's Jewish population.
"I want to see Mr. Rouhani and Mr. Obama sit in front of each other and speak about life," store owner Ali Hayati said.
"They realize that they need each other, they like each other, and they feel this is the right time to get together and start talking at least," retailer Sadegh Kiyaei said.
Secretary of State John Kerry is set to meet with Iran's foreign minister at this week's U.N. General Assembly meeting. It will be the highest level meeting between the US and Iran since the 1979 Iranian revolution.
