The US has applauded Iran's decision to free 15 British naval personnel but said the positive move would not ease tensions over its nuclear programme.
Mr Bush gave rare approval to an Iranian decision
President George W Bush welcomed the decision, his spokeswoman said.
But Washington reiterated it would only talk directly to Tehran if it suspends its uranium enrichment programme.
Vice President Dick Cheney said it was unfortunate the sailors were taken in the first place and he hoped there would be no exchange of favours.
"Once people start taking hostages or kidnapping folks on the high seas and then are rewarded for it by getting some kind of political concession... that would be unfortunate," Mr Cheney told ABC News.
He made it clear that Iran was in the wrong, saying there was considerable evidence the British sailors and marines were in Iraqi waters when arrested.
Announcing the release of the 15 Britons, Iran's President Mahmoud Ahmadinejad said Tehran could reconsider its relations with Washington if Mr Bush's attitude changed.
"The behaviour that needs to change is the Iranians, not the United States," said US State Department spokesman Tom Casey.
Mr Casey said the US would only deal directly with Iran if it suspended its controversial uranium enrichment activities and adhered to the UN Security Council resolutions.
Washington suspects Iran of seeking nuclear weapons. Tehran insists its nuclear programme is for peaceful purposes.
The former US ambassador to the UN told the BBC he believed Mr Ahmadinejad had been emboldened by the affair, and would now continue his pursuit of nuclear weapons capability.
"President Ahmadinejad... won by seizing British hostages and by unilaterally deciding to release them, having found out the answer to the question I think he was posing, which is - how strong a response will Britain make?
"The reaction was - not much at all. I think Ahmadinejad is actually emboldened in his pursuit of nuclear weapons, and I think that means more trouble ahead for all of us."
The timing is difficult for Washington as it is seeking Iranian help over a former FBI agent who disappeared in March on a business trip to Iran's Kish island, a free-trade zone in the Gulf where Americans do not need visas.
US officials believe the man, identified as Robert Levinson - an expert on organised crime and the Russian Mafia - may have been detained by Iranian officials.