It said the launch vehicle, named Simorgh after a bird in Iranian mythology, was capable of propelling a satellite weighing 250 kilograms to an altitude of 500 kilometres above earth.
The launch marked the official inauguration of Iran's Imam Khomeini space centre, named after the late founder of the Islamic republic, built for sending satellites into space, the television said, without giving its location.
Western states suspect Iran of developing the technology capable of launching long-range ballistic missiles with conventional or nuclear payloads, a charge denied by Tehran which insists its space programme has purely peaceful aims.
President Hassan Rouhani said yesterday that Iran would respond in kind to any breach by the United States of a 2015 nuclear deal after the House of Representatives passed a new sanctions bill.
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"If the enemy steps over part of the agreement, we will do the same, and if they step over the entire deal, we will do the same too," Rouhani said at a cabinet meeting.
The Iranian parliament's national security and foreign affairs committee said it would hold an extraordinary session on Saturday to discuss its formal response.
"We must always develop our defence capability and we will strengthen our defensive weapons regardless of the opinion of others," Rouhani said.
The US House passed a new sanctions bill on Tuesday targeting the Revolutionary Guards over its missile programme.
As part of its space programme, Iran has also sent two capsules into space, the first in February 2010 carrying a rat, tortoises and insects, and the other in January 2013 when a monkey was sent into space and returned to earth safely, according to official media.