But there is a big caveat: Half of the respondents in the IPPO poll either said they were undecided or declined to disclose their choice.
There are other warning signs for Rouhani. Out of the top three candidates, Raisi generated the most positive mentions on social media, while Rouhani drummed up the most negative sentiment, according to an analysis of about 60,000 Persian-language social media, blog and message board posts conducted by data measuring firm Babel Street between April 9 and May 10.
The results "point to Iranian's discontent with the status quo under Rouhani, even as election polls place him in the lead," Babel Street said in a report.
Social media analysis by the Eurasia Group shows Rouhani leading on momentum, but Raisi surging to a dead heat with the president on their ability to identify with voters' concerns. Taking into consideration a broader array of issues, social sentiment lends support to a Raisi upset.
Qalibaf's exit gives Rouhani a clearer path to victory by lowering the odds he'll face a runoff election, according to Eurasia Group. The perception that Raisi is a potential successor to Supreme Leader Ayatollah Ali Khamenei may also stir moderate and reformist voters to action, the risk consultancy concluded.
But Eurasia Group nevertheless lowered the probability of Rouhani's re-election to 60 percent based on growing efforts by conservative elites and security forces loyal to Khamenei to mobilize support for Raisi, along with a lack of reliable polling data and history of surprises in Iranian elections.Economics in focus
Rouhani himself took the country by surprise in 2013 after a late-stage surge. But he now faces the burden of defending his record. The economy has returned to growth and inflation has stabilized during his tenure, but unemployment remains high, particularly among youth.
Meanwhile, Raisi is pushing a populist economic message especially popular with largely conservative rural Iranians. The countryside's 90 percent voter participation rate dwarfs the 40 percent and 60 percent rates in large and small cities, respectively, where Rouhani can expect to garner many of his votes.
"Given the uneven quality of Iranian polling, Raisi's economic message could be getting more traction than we believe," Eurasia Group Chairman Cliff Kupchan said in a research note.
Still, Raisi's run has been "mediocre at best" and the candidate lacks charisma, according to Kupchan. He believes Khamenei's base would have to manipulate election results on a large scale to nudge Raisi to victory, something the regime is hesitant to do after mass protests erupted in the wake of the contested 2009 election.
Meanwhile, Rouhani gave a strong performance in a recent debate focused on the economy, Kupchan noted, and the president has even alluded to Raisi's roll in the mass execution of political prisoners 30 years ago — a hot button issue among Iranians.
But at least one analyst believes the focus on the economy may be overdone. Alex Vatanka, senior fellow at the Middle East Institute, said Iran's most reform-minded president, Mohammad Khatami, won the presidency 20 years ago and remains a political force not because he promised jobs, but greater freedom.
"That's in essence what the average voter in Iran wants: someone to come in and shake up the system. Rouhani has not been convincing them," he said.