(CNN) A video aired Wednesday by Iranian state television shows an American sailor apologizing for entering Iranian waters, an embarrassing development for a U.S. administration trying to paint the service members' quick release as a diplomatic victory.

"It was a mistake that was our fault and we apologize for our mistake," said the U.S sailor, who was identified by Iran's Press TV as the commander. "It was a misunderstanding. We did not mean to go into Iranian territorial water. The Iranian behavior was fantastic while we were here. We thank you very much for your hospitality and your assistance."

In the same Iranian television interview, the sailor said, "The Iranian patrol boat came out when we were having engine issues and had weapons drawn, so we tried to talk to them until more boats came out and took us in."

In contrast, U.S. officials have said that there were no signs that the incident was a hostile one, and have not cited a specific cause for the boat straying into Iranian waters.

It is not clear from the video -- which shows the lone female sailor wearing a head covering in accordance with Islamic tradition -- that the sailor was speaking voluntarily, and U.S. officials have not yet said under what circumstances the apology was delivered. A spokesman for Secretary of State John Kerry has made it clear he has not apologized to Iran.

"The video appears to be authentic, but we cannot speak to the conditions of the situation or what the crew was experiencing at the time," said U.S. Central Command spokesman Lt. Cmdr. Ben Tisdale in a statement. "The crew is currently undergoing the reintegration process and we will continue to investigate this incident. What matters most right now, however, is that our Sailors are back safely."

In addition, a CENTCOM official told CNN: "Clearly this staged video exhibits a sailor making an apology in an unknown context as an effort to defuse a tense situation and protect his crew."

The sailors were released Wednesday to the American naval fleet in the Persian Gulf after being captured by the Iranian Revolutionary Guard on Tuesday. Iranian authorities let the 10 detained sailors go free after determining that their vessels' entry into Iranian waters was unintentional.

U.S. denies it had issued apology

Earlier, the country's semi-official FARS News Agency, citing a statement from Iran's Revolutionary Guards Corps, said the sailors were released "after they extended an apology."

The statement went on to say, "The Americans have undertaken not to repeat such mistakes."

But the State Department rejected any notion that the United States had offered an apology.

"There is no truth in reporting that Secretary Kerry apologized to the Iranians," Kerry spokesman John Kirby told reporters, later tweeting that the claim had "zero" validity. "As the Secretary said in his statement this morning, he expressed gratitude to Iranian authorities for their cooperation in swiftly resolving this matter, and noted that the peaceful and efficient resolution of this issue is a testament to the critical role diplomacy plays in keeping our country safe, secure, and strong."

The White House said that its approach was vindicated with the rapid return of the sailors.

But several Republicans criticized President Barack Obama for not addressing the incident during his State of the Union on Tuesday night, which came shortly after the sailors and their two ships were taken.

"At the White House we reached the conclusion that further elevating the situation by including it in the State of the Union address would not be the most effective way for us to ensure the safe return of our sailors," White House spokesman Josh Earnest said. "And I think the outcome, which is the release of the sailors just hours after the President completed his address, is a pretty powerful endorsement of that strategy."

Another video of the captured sailors showed them on their knees with their hands on their heads.

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The video was aired just as Kerry credited diplomatic strength and newly developed ties with Iran in helping secure the quick and safe release of the sailors.

"These are always situations as everybody here knows which have an ability, if not properly guided, to get out of control," Kerry said in a speech at the National Defense University. "I'm appreciative for the quick and appropriate response of the Iranian authorities."

He said that "all indications suggest or tell us that our sailors were well taken care of, provided with blankets and food and assisted with their return to the fleet earlier today."

Iranian official says release a learning moment

Iranian Foreign Minister Javad Zarif, who has maintained open lines with Kerry and U.S. officials, made no mention of an apology in a tweet he sent after the sailors were released.

"Happy to see dialog and respect, not threats and impetuousness, swiftly resolved the #sailors episode. Let's learn from this latest example," Zarif wrote.

Happy to see dialog and respect, not threats and impetuousness, swiftly resolved the #sailors episode. Let's learn from this latest example. — Javad Zarif (@JZarif) January 13, 2016

Kerry said things might not have gone as smoothly before the United States opened dialogue with the country over its nuclear program, culminating in a deal to curb its operations reached between Iran and the United States along with five other world powers in July.

Defense Secretary Ash Carter told 200 troops gathered at Fort Campbell in Kentucky that he was pleased with how the situation was handled.

"Our highest commitment," he said, "is to the safety of all of you. Wherever we may ask you to go, the country will never leave an American service member behind."

But critics of the administration take issue with its characterization, and have slammed the White House for the incident and questioned its timing.

The seizure of the sailors came days before the nuclear deal is expected to go into force and sanctions on Tehran -- which will be lifted in exchange for Iran's freeze on its nuclear nuclear program -- are set to start being rolled back.

Iran indicated that it is still expecting the implementation of the Iran deal to begin.

Iranian Deputy Foreign Minister Abbas Aragchi says the U.N. nuclear watchdog agency will issue its final report Friday confirming Iran's implementation of the deal between Iran and the six world powers, according to Iran's semi-official FARS news agency

Aragchi added that Zarif and the E.U. High Commissioner for Foreign Affairs Frederica Mogherini will hold a joint press conference on either Saturday or Sunday to announce implementation of the deal and the date sanctions will be removed from Iran.

The capture of the Navy sailors was quickly seized on by U.S. opponents of the nuclear deal as the latest in a series of provocations by Tehran since the deal was agreed, which include aggressive attempts to wield power in its immediate neighborhood and conduct ballistic missile tests that the United Nations claimed violated a Security Council resolution.

"This kind of openly hostile action is not surprising. It's exactly what I and so many others predicted when President Obama was negotiating the nuclear deal with Iran -- thast it would embolden their aggression towards the United States and our allies in the region," Arkansas Republican Sen. Tom Cotton told CNN's Wolf Blitzer on "The Situation Room" on Tuesday.

Other Republicans said the release of the video was a further rebuttal of the Obama administration's attempts to play down the incident.

"It's horrible. This is not what friendly nations do, especially if this was about a mechanical failure. You don't detain a friendly neighbor or friendly nation's armed forces and detain them overnight when you have friendly relations," Rep. Patrick McHenry, a North Carolina Republican, said on CNN's "Legal View."

Release dragged on for hours

A Navy statement said the detained sailors have been transferred to shore and are no longer on the guided-missile cruiser USS Anzio, which helped carry them back to U.S. custody.

The sailors were captured after their two naval boats entered Iranian waters near Farsi Island, in the Persian Gulf.

The wait for the sailors' release Wednesday morning dragged on for hours, with Iranian officials interrogating the sailors about their motives and demanding a U.S. apology.

But an Iranian Revolutionary Guard Corps spokesman told state-run media the boats strayed into Iranian waters by accident.

"The evidence suggests that they unintentionally entered the Iranian waters because of the failure of their navigational system," IRGC spokesman Ramazan Sharif said.

On Wednesday afternoon, the sailors traveled on their two boats to a rendezvous point in the Persian Gulf, a U.S. official said. They were escorted by Iranian boats, which turned back when they reached the rendezvous point in international waters.

The sailors boarded the USS Anzio, where they underwent medical checks.

"There are no indications that the sailors were harmed during their brief detention," the U.S. Navy said in a statement.

Navy investigation

The Navy said it would investigate how the sailors ended up in Iranian territory.

White House Chief of Staff Denis McDonough credited Kerry's work opening communications with Zarif through the nuclear deal negotiations with securing the quick release of the sailors.

McDonough said that facts were still being collected and the Navy was investigating the incident, but he said it was too early to make draw other lessons from the incident.

On Wednesday morning, officials interrogated the sailors to see whether they "entered Iranian waters intentionally on an intelligence mission," the IRGC said, according to state-run Press TV.

IRGC Navy commander Adm. Ali Fadavi said the presence of the U.S. Navy in the Persian Gulf waters "disturbed the security of the area" and criticized the U.S. Navy maneuvers.

What the ships were doing

The vessels were en route from Kuwait to Bahrain and were sailing near Farsi Island in the Persian Gulf.

A senior defense official told CNN the boats were in the area of Farsi Island for refueling, but it's not clear whether they actually refueled -- raising the possibility they ran out of fuel.

Another senior defense official said no distress call came from the boats.

Iran's official IRNA news agency reported that the boats were "rescued" by Iranian navy sailors.

There is nothing to indicate the capture was a hostile act on the part of Iran, a senior Obama administration official said.

The upcoming implementation of the nuclear deal might be why the U.S. sailors were held for only one day, a CNN military analyst said.

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"I certainly think they were released quickly because of the ongoing Iran deal," retired Lt. Gen. Mark Hertling said.

He noted that when British sailors were captured by Iran in 2007, they were held for about two weeks.

"I think there potentially is a new age coming about with Iran," Hertling said. "This is going to improve military-military relationships."

Previous captures

In 2004, three British patrol boats were boarded and seized by Iranian security forces in the Shatt al Arab waterway, which divides Iraq and Iran. The crews of the three boats, including eight British sailors and marines, were blindfolded and paraded on Iranian state TV and held captive for three days.

In 2007, Iran captured 15 British sailors and marines in the Persian Gulf and accused them of trespassing in Iranian territorial waters. Britain maintained that its service members never entered Iranian waters.

Those British service members were paraded before then-President Mahmoud Ahmadinejad, and critics said their apologies were extracted under duress. They were released after two weeks.

After the 2007 capture, Adm. Mike Mullen, who was U.S. chief of naval operations at the time, said, "We've got procedures in place which are very much designed to carry out the mission and protect the sailors who are there, and I would not expect any sailors to be able to be seized by the Iranian navy or the Iranian Republican Guard."