Rouhani, a politically moderate cleric, has won praise since his landslide win in 2013 for taming inflation and reaching a groundbreaking nuclear deal with world powers that ended many sanctions.
But disappointment over Iran's continued economic stagnation is palpable on the streets, creating an opening for conservative opponents, with judicial cleric Raisi emerging as their frontrunner.
Unemployment is stuck at 12 percent, the promised billions in foreign investment have not materialised, and Rouhani has failed to release political prisoners, including reformist leaders under house arrest for their part in 2009 protests.
The aggressive stance of US President Donald Trump, who has slapped new sanctions on Iran and threatened to tear up the nuclear deal, has bolstered conservative claims that Rouhani was duped by the West.
Rouhani, 68, hit back on Friday, saying: "The preservation of the (nuclear deal) is one of the most important political and economic issues in the Iranian nation. The stepmothers who repeatedly tried to kill this baby cannot be good custodians for it."
He said an "unprecedented" $20 billion worth of new projects would be announced next week, which would also see gas production at the South Pars field surpass that of Qatar -- which shares the field -- for the first time.
That follows government plans, outlined this week, to triple or even quadruple cash hand-outs to the poor -- a move immediately criticised by opponents as a transparent attempt to buy votes.
- Raisi's emergence -
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The conservatives remain divided, but Raisi appears to have the most momentum.
The 56-year-old judge, who currently runs the powerful charity-cum-business-empire Astan Qods Razavi, has emphasised his concern for the poor and is seen as a close ally of supreme leader Ayatollah Ali Khamenei.
He sought to reach across political lines on Friday, saying: "I will be the candidate for the whole of Iran. I don't limit myself to a certain group, party or faction.
"Despite all the efforts of previous governments, the situation of the country is such that people ask why is there so much unemployment?" he said, adding that he would announce detailed economic plans at a later date.
A potential spoiler appeared on Wednesday, when former hardline president Mahmoud Ahmadinejad made the shock move of registering for the election against Khamenei's advice.
A clearer picture will emerge next week when the conservative-controlled Guardian Council announces which of the near-1,000 registered candidates are allowed to run in the May 19 election.
Ardavan Amir-Aslani, a French-Iranian lawyer who advises European companies setting up in Iran, said he would be surprised if Rouhani does not win re-election despite the economic malaise.
"He has at least stabilised the economy... and created a better business environment. But Rouhani has not been successful in opening up foreign investment," he told AFP.
"He inherited a bad situation, but he created so much expectation and nothing has changed for the guy on the street."
Rouhani has also lost one of his main backers: heavyweight former president Akbar Hashemi Rafsanjani, who passed away in January, played a key role in the surprising landslide victory in 2013.
But, crucially, Rouhani retains the unified support of moderates and reformists, who still see him as the best hope for change within the strict parameters of Iran's Islamic system.