Much of Iran's uranium enrichment takes place at the Natanz plant
G8 leaders are "seriously concerned" about the "appalling events" after Iran's elections, US President Barack Obama said as the summit closed.
He said the global leaders were also "deeply troubled" by Iran's nuclear programme. Iran denies claims it is trying to build a nuclear bomb.
Mr Obama rebuffed suggestions that the summit had fallen short in failing to agree fresh sanctions in Iran.
The G8 leaders said they would review Iran's progress in September.
A joint declaration from the summit in L'Aquila, Italy, said that media restrictions and the detention of foreign nationals by Iran was "unacceptable".
Iran has recently released eight of nine British embassy staff that it arrested and accused of spying during protests against the alleged rigging of presidential elections last month.
But one Briton and a French language teacher, Clotilde Reiss, 23, remain in Iranian custody.
On Friday, French Foreign Minister Bernard Kouchner called for her release and said espionage accusations against her were "stupid".
Israel 'not alone'
The G8's joint declaration warned Tehran to comply with UN resolutions calling for a freeze on its uranium enrichment activities - a process which can be used to make material for a nuclear bomb - "without further delay."
Speaking on Thursday, French President Nicolas Sarkozy warned that a unilateral Israeli military strike on Iran's nuclear facilities would be an "absolute catastrophe".
But he reassured Israel that it was "not alone".
Mr Sarkozy threatened further sanctions against Iran if it failed to respond to US overtures for talks on its nuclear activities.
Mr Obama said the international community would not wait "indefinitely" for Iran to comply with its demands.
The joint declaration said the leaders would "take stock" of whether Iran had complied with demands for a freeze on its nuclear activities at the G20 meeting in Pittsburgh in the US in September.
"Between August and September it's for them to decide how they want things to evolve. Pittsburgh is the date," said Mr Sarkozy.
The summit follows pledges earlier this week by the US and Russia to cut their stockpiles of nuclear weapons.
Mr Obama is planning an international conference on nuclear proliferation in March 2010.