Rouhani rejected criticism from conservatives over his economic performance, saying he had overseen measurable improvements in agriculture, health care, energy and internet coverage.
He also focused on his key achievement, a nuclear deal with world powers that ended some sanctions in return for curbs on Iran's atomic programme.
"In every aspect that you consider, figures tell us that after the (nuclear deal), there is more space for movement and progress," he said.
Pointing to deals signed by Iranian airlines to buy planes from Airbus and Boeing, he said the some $4 billion (3.8 billion euros) that Iranians spend on tickets to fly abroad would now go to domestic carriers.
Rouhani is expected to run for a second term on May 19, but said this press conference was "not about elections".
"We need to wait two or three more days," he said.
Hopefuls in the election have from Tuesday until Saturday evening to register their candidacy.
Sitting presidents in Iran are expected to be modest about their ambitions and to refrain from using state television as a campaigning platform.
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The moderate cleric boasted that his government had allowed social media platforms to stay online despite objections from conservatives.
"People should speak out clearly about issues that are not being handled to their satisfaction," he said.
He criticised the arrests of administrators of top reformist social media channels in late March.
Rouhani also slammed the United States for imposing sanctions on Iran and attacking an airbase in Syria, a key Iranian ally, following a suspected chemical attack last week.
"The Syrian people and army must give a response that makes Americans regret their attack," he said.
During his first month in office, US President Donald Trump imposed fresh sanctions targeting Iran's ballistic missile programme.
Rouhani said America had "never acted within international frameworks".
"One instance is the sanctions it has imposed on Iran, unreasonably seeing itself as the leader of the world," he said.
Rouhani said Tehran was "ready to improve relations" with regional arch-rival Saudi Arabia providing Riyadh "stops its attacks on Yemen" where a Saudi-led coalition is battling Iran-backed Huthi rebels.
The Sunni kingdom cut diplomatic ties with Shiite-dominated Iran early last year after its missions were attacked in Tehran and Mashhad by protestors angered at Riyadh's execution of a prominent Shiite cleric.