The remarks showed a widening rift between Rouhani and hardliners, especially the Supreme Leader Ayatollah Ali Khamenei who has called himself a proud revolutionary in recent months.
"What's the use of saying I am a revolutionary ... Why don't we seek people's comfort and our country's glory?" Rouhani said in a speech broadcast live on the state television.
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Rouhani has championed the nuclear deal with six major powers that put an end to international sanctions on Tehran in January, and has been since trying to revive Iran's business and political ties with the West.
Moderates and reformers also saw big gains in February elections for parliament and for the Assembly of Experts - a body that will choose the next supreme leader.
Hardline allies of Khamenei have accused him of betraying the anti-Western values of the 1979 revolution that toppled the US-backed Shah.
But Rouhani said the election results were new vote of confidence for his policies and promised to push for more political and social reforms.
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"We had a revolution to promote morality, national unity, and brotherhood... You are a revolutionary when people feel safe from your words and actions," Rouhani said.
Criticising hardline newspapers that have increased their pressure on Rouhani's allies in recent months, he said: "Some newspapers are bulletins of insult. You open them anxiously to see how they have insulted you again. Is this Islam, is this Islamic society?"
Last week Khamenei told Assembly members to choose a "revolutionary" successor to him when the time saying, saying the next supreme leader should not compromise on Iran's stance against the United States.
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Khamenei said Iran's economy had not yet benefited from the Western delegations visiting Iran after the lifting of sanctions as they had failed to deliver on their promises. He added he saw some of the visits as suspicious as the West was trying to send "infiltrators" in disguise.
During the nuclear talks led by the United States, Khamenei repeatedly told his supporters that he did not trust the West and that he was "still a revolutionary, not a diplomat".
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