President Hassan Rouhani congratulated the scientists involved in the mission, in a message carried by Iran's official IRNA news agency.
In January, Iran said it had successfully brought a live monkey, which it named Pishgam (pioneer), back to Earth from orbit.
But the experiment's success was disputed, when a different monkey was presented to the media after the landing.
An earlier attempt had failed in September 2011.
Iran's space programme has prompted concern among Western governments, which fear Tehran is trying to master the technology required to deliver a nuclear warhead.
"By the grace of God and through the efforts of Iranian space scientists, the Pajohesh (research) rocket containing the second live space monkey, named Fargam (Auspicious), was sent into space and brought back to Earth safely," Rouhani said in his message.
Iran's space programme was heavily promoted by Rouhani's controversial predecessor Mahmoud Ahmadinejad, who quipped in February that he was "ready to be the first Iranian to be sacrificed by the scientists of my country and go into space, even though I know there are a lot of candidates."
To the dismay of animal welfare groups, Fargam was following in the footsteps of a menagerie of dogs and monkeys who were among the early stars of the US and Soviet space programmes in the 1960s.
Earlier this year, Iranian space officials raised the prospect of sending a Persian cat into space.
"Iran's archaic experiment... is a throwback to the primitive techniques of the 1950s," People for the Ethical Treatment of Animals spokesman Ben Williamson said at the time.
The stated aim of Iran's programme is a manned launch by 2020.
The programme deeply unsettles Western governments as the technology used in space rockets can also be used in ballistic missiles.
The UN Security Council has imposed an almost total embargo on the export of nuclear and space technology to Iran since 2007.
Tehran denies its space programme has any link with its alleged nuclear ambitions.
COMMENTS (5)
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Impressive. Don't be fooled by the biased reporting from agencies. This is a big achievement.
Bad time to be a monkey in iran.
I am as confused as the monkey itself. So, Iran sent the 1st monkey into space and showed the world the 2nd monkey because they couldn't produced the 1st monkey. So, now, this 2nd monkey is the same 2nd monkey which was displayed on TV, or it is the 3rd monkey? And, where is the 1st monkey? They left him up in the space?
And we sent one to India.