Secretary of State John Kerry said the resolution of the matter was “testament to the critical role diplomacy plays in keeping our country safe”.
Republican presidential hopefuls had criticised the administration over its handling of the incident.
A deal on Iran’s nuclear activities – which they also disparage – is said to be days away from implementation.
The sailors were detained on Tuesday when one of their two vessels broke down while training in the Gulf.
The incursion was “unintentional”, a statement from the Iranian Revolutionary Guards quoted by state media said.
Iranian state media said the sailors were released into international waters after they apologised. But Vice-President Joe Biden denied this, saying the boat had had simply a problem and there was “nothing to apologise for”.
The US is investigating how the sailors entered Iranian waters.
Thanking Iranian authorities for their “co-operation and quick response”, Mr Kerry said: “These are always situations which have an ability if not properly guided to get out of control…
“This kind of issue was able to be peacefully resolved and officially resolved, and that is testament to the critical role diplomacy plays in keeping our country safe, secure, and strong,” he added.
Iranian state broadcaster Irib News has published pictures of the sailors apparently being detained
Later pictures published on the Revolutionary Guards’ website showed the group sitting on a Persian rug, with the one female member wearing a headscarf.
Mr Kerry called Foreign Minister Mohammad Javad Zarif shortly after the incident. The pair developed a personal rapport during the nuclear talks.
Those detained – nine men and one woman – were taken to Farsi Island, in the middle of the Gulf, where Iran has a naval base.
Conservatives in both countries have opposed the nuclear deal, under which Iran will limit its nuclear activities in exchange for the lifting of sanctions.
In the US, Republican presidential candidates were among those expressing outrage at the sailors’ detention.
“Iran is testing the boundaries of this administration’s resolve,” said Marco Rubio.
“[Barack] Obama’s humiliatingly weak Iran policy is exposed again,” Jeb Bush said in a tweet before the sailors were released.
Donald Trump said Iran was “toying” with the US.
Iran’s deputy nuclear chief has meanwhile denied a report the Arak heavy-water reactor had been decommissioned, which would be a final step towards implementation of the nuclear deal.
Source BBC
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