U.S. officials are pointing the finger at elite Iranian military forces for the sabotage attacks on oil tankers near the Persian Gulf.

A week after claiming Iranian "preparations for possible attack" on U.S. forces in the region, the U.S. has ordered most State Department personnel out of neighboring Iraq.

U.S. and Iranian officials insist nobody wants a war, and President Trump has denied plans to send 120,000 troops to the region.

The U.S. military has refuted a senior British commander's assessment that there has been "no increased threat from Iranian-backed forces in Iraq and Syria."

U.S. officials have said they believe Iranian combat divers were behind the attacks on four oil tankers near the Persian Gulf over the weekend, and they tell CBS News senior national security correspondent David Martin there's still no sign Iran is backing off purported plans to attack Americans in the region.

Martin said American officials have him there is "credible" and "urgent" intelligence that Iran has ordered Shiite militias in Iraq to prepare to conduct attacks against U.S. troops and diplomats in the country.

On Wednesday the State Department ordered all non-emergency staff and their families to leave Iraq, a nation on Iran's southern border in which the Iranian government backs various militia groups which have fought U.S. troops before.

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"U.S. citizens in Iraq are at high risk for violence and kidnapping. Numerous terrorist and insurgent groups are active in Iraq and regularly attack both Iraqi security forces and civilians. Anti-U.S. sectarian militias may also threaten U.S. citizens and Western companies throughout Iraq," the State Department said in its advisory.

Secretary of State Mike Pompeo renewed the Trump administration's warning on Tuesday that the U.S. would retaliate against Iran if it does attack American interests in the Middle East, but he declined to pin the blame for the tanker sabotage on Tehran.

He said he didn't have anything "concrete about the connection" between Tehran and the tanker attacks, adding: "I think in the coming hours and days we'll know the answer to that."

At a campaign rally on Tuesday evening, President Trump emphasized what is becoming one of the hallmarks of his hardline foreign policy, telling supporters that his administration was "holding dangerous regimes accountable by denying them oil revenue to fund their corruption, oppression and terror."

But as Martin reports, while the U.S. has put a stranglehold on Iran's economy, the country remains dangerous.

U.S. officials told Martin it was highly likely that Iran's Islamic Revolutionary Guards were responsible for Sunday's attacks that blew holes in the hulls of Saudi and Norwegian tankers anchored off the Emirati port of Fujairah, just outside the Persian Gulf.

Iranian combat divers are believed to have attached explosives to the ships' hulls, but a defense official told CBS News that further investigation was still needed.

Trump sending troops to Iran?

Mr. Trump, meanwhile, dismissed a New York Times report saying the administration was planning to send 120,000 American troops to the region to counter Iran. The U.S. has already sent an aircraft carrier strike group and four B-52 bombers to the Persian Gulf.

President Trump's denial of the Times report came with a caveat: "Would I do that? Absolutely," he said as he left the White House on Tuesday. "We have not planned for that… and if we did that, we'd send a hell of a lot more troops that."

On Capitol Hill, Virginia Democratic Senator Tim Kaine blasted the president's thinking.

"It would be the height of idiocy. It would be unconstitutional. There's no way this president should get us into a war with Iran," Kaine said.

Iran escalates nuclear threat

Iran has vehemently denied being involved in the attacks on the oil tankers and accused President Trump of playing a "very dangerous game, risking devastating war."

But on Wednesday, Iran's Supreme Leader Ayatollah Ali Khamenei said: "There is not going to be a war. Neither are we seeking war, nor is it to their (the United States') benefit to go after a war. They know this. We never start a war and have never started any wars. This is a confrontation of will-powers and our will-power is stronger than theirs."

He ruled out any negotiations with the current U.S. administration, saying they would be "poison" for Iran.

But while he downplayed the possibility of a conflict with the U.S., the ayatollah also dropped a loosely-veiled threat that Iran could take steps -- within a few months -- that would almost certainly draw a significant American response.

Iran announced a week ago that in response to President Trump pulling the U.S. out of the nuclear deal agreed in 2015 with world powers, it would partially withdraw from the terms of the agreement, too.

The Iranian regime said if the other parties to the agreement, which still want to keep it viable, couldn't figure out a way to work around new U.S. sanctions to keep doing business with Tehran within 60 days, it would resume enriching uranium to levels barred under the deal.

Iran is permitted under the terms of the nuclear deal to enrich uranium to just under 4% concentration -- a level at which it can be used for medical and scientific purposes, but not be easily refined to a level required to make nuclear weapons.

The regime said if no agreement was reached with Europe, Russia and the Chinese to keep the 2015 deal in play, it would resume enriching uranium to 20% -- which officials in the country have said could be done within four days. That benchmark is significant because once uranium is refined to 20%, it becomes much easier to enrich it to the 90% needed for weapons.

On Wednesday, the Ayatollah said "achieving 20% enrichment is the most difficult part. The next steps are easier than this step."

It was the first hint from the Iranian regime that it might try to obtain the highly-enriched uranium needed for an atomic bomb -- though Iranian officials have always denied any interest in obtaining one.

Both the U.S. and Israel have made it clear they will not allow the Islamic Republic to obtain a nuclear weapons capability.

U.S. and allies on same page?

There have been signs of frustration from European allies over the Trump administration's decision to not only bail on the nuclear deal, but to mount the new pressure on the Iranian regime.

The Trump administration and U.S. military officials said just over a week ago that they had detected, "a number of preparations for possible attack" on U.S. forces at sea and on land in the Middle East.

The U.S. has about 5,000 troops still in Iraq, on Iran's border, and while the State Department order on Wednesday for non-emergency personnel to leave the country did not specifically mention a threat from Iran, that was the implication.

Again without specifically citing Iran, a spokesperson at the U.S. Embassy in Iraq told CBS News on Wednesday that Pompeo ordered the non-emergency U.S. personnel out of the country because, "these threats are serious."

British Maj. Gen Christopher Ghika, Deputy Commander-Strategy and Information for the Combined Joint Task Force - Operation Inherent Resolve, the U.S.-led military operation in Iraq, is seen in a handout photo. HANDOUT

On Tuesday, however, a British deputy commander of the U.S.-led joint military operation in Iraq disputed the claim of an elevated threat to allied forces in the region.

"There's been no increased threat from Iranian-backed forces in Iraq and Syria," Maj. Gen Christopher Ghika said in a video briefing from Baghdad to the Pentagon, according to The Guardian. "We're aware of that presence, clearly. And we monitor them along with a whole range of others because that's the environment we're in. We are monitoring the Shia militia groups I think you're referring to carefully, and if the threat level seems to go up then we'll raise our force protection measures accordingly."

But the U.S. military's Central Command, which oversees Operation Inherent Resolve (OIR) in Iraq and all other American operations in the region, directly refuted Ghika's statement later on Tuesday.

"Recent comments from OIR's deputy commander run counter to the identified credible threats available to intelligence from US and allies regarding Iranian-backed forces in the region," Central Command spokesman Capt. Bill Urban said in the statement.

One U.S. officer told Martin he was "flabbergasted" by the British commander's assessment.

Martin said the Pentagon has released very little detail of the intelligence pointing to the purportedly heightened threat from Iran, "and without the details it's easy to become skeptical about exactly how good the intelligence is."

But Martin said he had spoken to multiple U.S. military officials, including some who privately disagree with the Trump administration's policy in Iraq, and that they all agreed there is intelligence pointing to possible attacks by Iranian proxy groups which appears credible.

Germany's military, meanwhile, announced a halt to its training operations in Iraq on Wednesday, but said it had no information about heightened threats to German troops in the country from Iran.

Defense Ministry spokesman Jens Flosdorff cited heightened regional tensions as he confirmed Germany's military was temporarily suspending training of Iraqi forces, "orienting itself toward our partner countries," but adding there were "no concrete warnings of attacks against German targets."

The Netherlands made a similar announcement, putting its training operations on hold citing an unspecified security threat, but France defense officials said their training mission in Iraq was continuing unaffected.