"It is not going to get any better than this. It's not going to get better than an American administration saying we want normal relations with Iran," Miliband told an international security conference in Munich, Germany.
He also urged his European allies to do more to back the new US administration of President Barack Obama, by ensuring that Iran could face sanctions if it does not seize this opportunity.
"We in Europe, while applauding the determination of the United States to stretch out a hand to Iran, have got to realise that the United States will be far, far better off in reaching out that hand if they're able to say: 'if we're not met by an outstretched hand from Iran, very serious and very tough sanctions will follow'," he said.
Major world powers have offered the Islamic republic a package of political and economic incentives to suspend uranium enrichment, which at highly refined levels can be used to fuel an atomic bomb.
But Iran maintains that it is only trying to develop a civilian energy generation programme, and refuses to suspend enrichment as a condition for any talks, even as it labours under UN sanctions.
"All our experience with Iran suggests that if it's incentives only, it's not going to work," said Miliband, whose country is a permanent member of the UN Security Council.
He said that he had hoped to deliver the message in person to Iranian parliament speaker and former top nuclear envoy Ari Larijani, who was also taking part in the meeting.
