A video of US sailors in Iranian custody stirred outrage among Republican presidential candidates Thursday, while the government denounced Tehran's use of the images for propaganda even as it insisted on improved relations.

During a debate of Republican presidential candidates Thursday, Senator Ted Cruz said many citizens were "horrified to see the sight of 10 American sailors on their knees, with their hands on their heads."

He denounced President Barack Obama for not mentioning the sailors during his annual State of the Union address Tuesday while they were in Iranian custody.

"I give you my word, if I am elected president, no serviceman or servicewoman will be forced to be on their knees, and any nation that captures our fighting men will feel the full force and fury of the United States of America," Cruz said.

New Jersey Governor Chris Christie tied the incident to Obama's decrease of military spending.

"We need to rebuild our military, and this president has let it diminish to a point where tinpot dictators like the mullahs in Iran are taking our Navy ships," he said.

US Defence Secretary Ashton Carter said the government was investigating the detention of two US vessels, and was "very glad" to have the sailors back. They were released after 16 hours in Iranian custody.

A video of the nine men and one woman kneeling with their hands over their heads renewed concerns among lawmakers about the Obama administration's policy of improving relations and the nuclear deal signed by Tehran in July with six world powers.

"Obviously, I don't like to see our people being detained by a foreign military," Carter said. But he insisted that it was important to know "the full context" of the incident.

"What you're looking through in those [video images] is the lens of the Iranian media," he said.

The sailors should be given an opportunity to explain what happened, Carter said.

US officials previously said a "navigational error" had caused the two vessels to drift into Iranian waters, but Carter said Thursday there appeared to have been a combination of factors.

He said the Pentagon was still talking with the crew about what happened, but said the sailors were "clearly out of the position that they intended to be in."

The incident occurred at a key stage in the Iran nuclear deal.

Tehran is dismantling nuclear activities in exchange for the lifting of international sanctions.

US State Department spokesman John Kirby said the implementation "will occur very soon."

Kirby confirmed that concrete has been poured into a nuclear reactor slated for decommissioning under the pact.

Iranian Foreign Minister Mohammad Javad Zarif tweeted that he was pleased that dialogue and respect resulted in the quick release of the US sailors.

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