The Fajr (Dawn) satellite was successfully placed 450 kilometres above Earth, said Al-Alam television, an Arabic-language station owned by the Islamic republic.
It is the fourth such satellite launch by Iran, after three others between 2009 and 2012.
The satellite was locally made, said the official IRNA news agency, as was its launcher, according to Rouhani who noted Iran's aim is to have no reliance on foreign space technology.
"Our scientists have entered a new phase for conquering space. We will continue on this path," Rouhani said in a short statement on state television.
The launch came as Iran started 10 days of celebrations for the 36th anniversary of the Islamic revolution, culminating on February 11, "Victory Day," when the US-backed shah's reign officially ended in 1979.
Defence Minister General Hossein Dehgan echoed Rouhani's comments, stating that the 21-metre and 26 tonne launcher, named Safir-Fajr, shows "the ability of Iran to build satellite launchers".
In February 2010, Iran launched a satellite containing a rat, turtles and insects.
Iran's space activities, however, have sent alarm bells ringing in the international community amid concern over Tehran's development of technology that could have military purposes.
Some Western countries suspect Iran of secretly trying to build an atomic bomb and fear the technology used to launch space rockets could be diverted into developing long-range ballistic missiles, potentially capable of carrying atomic warheads.
Tehran has long denied having military goals for its space programme or its nuclear drive, and is currently engaged in talks with the United States and other leading powers to end the standoff over its disputed atomic activities.
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