"I request that the 40th year of the revolution, the coming year, be the year of unity. I ask conservatives, reformists, moderates and all parties and all people to come and be together," he said in a speech before a huge crowd in Tehran.
Rouhani, a long-time regime insider who won power in 2013 and again in 2017 with the backing of reformists, has faced tough criticism from conservatives over his efforts to rebuild relations with the West and ease civil liberties.
He has tried to use protests that hit dozens of cities over the new year as a way to convince conservatives that they must follow his calls for reform.
"We should trust the people. We must allow all inclinations to participate in elections," he said in an apparent swipe at the conservative-dominated Guardian Council, which regularly blocks hundreds of reformist candidates from standing in presidential and parliamentary votes.
"Our revolution was victorious when we were all together," he said.
"And today we must once again invite everyone to get on board the successful and victorious train of the revolution.
"All Iranian races, all Iranian religions, Shiites and Sunnis, Muslims, Christians, Jews and Zaroastrians - whoever believes in the constitution, that is our criteria. He is a revolutionary and he must be respected," Rouhani said.