"As the sun is about to set here in Tehran I wish all Jews, especially Iranian Jews, a blessed Rosh Hashana," he posted Wednesday.
The greeting by Rouhani contrasts with his predecessor, Mahmoud Ahmadinejad, who denied the Holocaust and called for the elimination of Israel.
"Not even under the monarchy do we remember such a message," Haleh Esfandiari, an Iranian-born scholar who heads the Middle East program at the Woodrow Wilson International Center, told al-Monitor.
Later this month, Rouhani will be in New York to address the U.N. General Assembly and participate in a disarmament meeting.
Israel warned that Rouhani's positions aren't that different from his predecessor despite the "moderate" label, Israeli broadcaster Artuz Sheva reported.
As an example, Artuz Shiva said Rouhani recently said Iran was prepared for "serious" discussions about its nuclear program and that U.S. calls for tougher sanctions demonstrated a lack of understanding. However, Rouhani said soon after his election Tehran would not consider ending the country's uranium enrichment activities entirely.