Speaking outside Downing Street this evening, Mr Blair stopped short of thanking the Iranian president, but said he had taken a "measured approach" in seemingly ending the dispute, "firm but calm, "not negotiating but not confronting either".
In a direct message to the Iranian people, the prime minister insisted on behalf of Britain: "We bear you no ill will.
"We respect Iran as an ancient civilization and as a nation with a proud and dignified history," he said.
"The disagreement we have had with your government, we had always hoped to resolve peacefully and with dialogue."
Mr Blair added: "We hope in the future to be able to do so also."
Flanked by foreign secretary Margaret Beckett, the prime minister thanked the EU and the UN security council for supporting Britain during the crisis.
He went on to thank "our friends and allies in the [Middle Eastern] region who have played their part; we are grateful to all of them and also to our officials at the Foreign Office, the Ministry of Defence and Downing Street".
The 15 Royal Navy personnel are expected to fly to Britain from Tehran tonight.
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