United States President Donald Trump says Iran appears to be "standing down" and no Americans have been harmed in ballistic missile strikes on two Iraqi bases housing US troops.

Key points: Mr Trump declared additional economic sanctions on Iran

Mr Trump declared additional economic sanctions on Iran He stopped short of making any direct threat of military action against Iran

He stopped short of making any direct threat of military action against Iran The Iranian strikes had come days after Mr Trump authorised the killing of General Qassem Soleimani

Speaking for the first time since Iran's attack, Mr Trump opened up his White House address shortly after 11:30am on Wednesday (local time) saying, "As long as I'm President of the United States, Iran will never be allowed to have a nuclear weapon".

"No Americans were harmed in last night's attack by the Iranian regime. We suffered no casualties," Mr Trump said during the address, which signalled a desire to de-escalate the crisis with Iran.

Mr Trump also declared the US would impose additional economic sanctions on Iran and that he would personally, "ask NATO to become much more involved in the Middle East process".

"The fact that we have this great military and equipment, however, does not mean we have to use it. We do not want to use it. American strength, both military and economic, is the best deterrent," he said.

He added that Americans should be "extremely grateful and happy" with the outcome.

Mr Trump stopped short of making any direct threat of military action against Iran.

He urged world powers, including Russia and China, to abandon the 2015 nuclear accord with Iran and work toward a new agreement.

"We must all work together toward making a deal with Iran that makes the world a safer and more peaceful place," he said.

A satellite image taken hours after a reported Iranian attack on the Al Asad air base in Iraq show several impact sites. ( Planet Labs )

Iran fired 16 short-range ballistic missiles from at least three locations inside Iran, US Defence Secretary Mark Esper told reporters at the Pentagon on Wednesday (local time).

At least 11 of them hit the Al Asad airbase, while at least one other missile hit a facility in Erbil, Iraq. The others failed in flight.

Mr Esper said missiles hit tents, a helicopter and a parking lot but there was no major damage.

Strikes a retaliation to US killing of General Soleimani

Erbil airbase and Al Asad airbase were hit in the attacks. ( ABC News )

The Iranian strikes came days after Mr Trump authorised the targeted killing of General Qassem Soleimani, the head of Iran's elite Quds Force.

Iran's Supreme Leader, Ayatollah Ali Khamenei, addressed a gathering of Iranians chanting "Death to America" earlier on Wednesday and said Iran's attacks were a "slap on the face" against the United States and urged US troops to leave the region.

Iranian Foreign Minister said Iran took "proportionate measures" in self-defence and did not seek an escalation.

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Iranian state television said Iran had fired 15 ballistic missiles from its territory at US targets in its neighbour Iraq early on Wednesday.

Iranian state television had said 80 "American terrorists" had been killed and US helicopters and military equipment had been damaged. But it did not say how it obtained that information.

Australia, Germany, Denmark, Norway and Poland said none of their troops in Iraq were hurt.

Britain, which also has personnel in Iraq, condemned the Iranian action and said Tehran, "should not repeat these reckless and dangerous attacks".

Iraq said its forces did not suffer casualties.

More than 5,000 US troops remain in Iraq along with the other foreign forces in a coalition that has trained and backed Iraqis against the threat of Islamic State militants.

Iran strikes intended to kill: US military

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Watch Duration: 2 minutes 5 seconds 2 m 5 s Iranian Revolutionary Guard missiles hitting Al Asad airbase

Mr Trump's reaction in the immediate aftermath of the attacks had been to say on Twitter, "All is well!" and that Washington was assessing the damage.

His early tweet and the comment by Iran's Foreign Minister about not seeking retaliation had acted to soothe some initial concerns about a wider war and calmed jittery financial markets.

US and European government sources said they believed Iran had deliberately sought to avoid US military casualties in its missile strikes to prevent an escalation.

But a top US military official said Iran's missile attack had intended to kill US personnel as well as cause major damage at Al Asad airbase, adding it was still too early to tell if Iran would carry out additional attacks.

"I believe, based on what I saw and what I know, is that [the strikes] were intended to cause structural damage, destroy vehicles and equipment and aircraft and to kill personnel. That's my own personal assessment," Army General Mark Milley, chairman of the Joint Chiefs of Staff, told reporters.

"But the analytics is in the hands of professional intelligence analysts. So they're looking at that."

General Milley commended the military commanders on the ground for taking appropriate action to safeguard US personnel.

He said he and others in the military "fully expect" Shiite militia groups in Iraq, backed by Iran, to carry out attacks against US and US-led forces in Iraq and Syria: "That's a very real possibility."

Mr Trump, who was impeached last month and faces an election this year, had threatened to target 52 Iranian cultural sites if Iran retaliated for General Soleimani's killing.

On Wednesday, an Iranian army spokesman had denied "foreign media reports" suggesting there had been some kind of coordination between Iran and the US before the attack to allow bases to be evacuated, Iran's Fars news agency said.

The Al Assad airbase in Iraq was targeted by Iranian missile strikes. ( AP: Nasser Nasser )

Iraq's Foreign Ministry said it rejected Iran's missile attack on Iraqi military bases housing US troops and would summon Tehran's ambassador in Baghdad to convey its protest.

"The Foreign Ministry rejects these attacks and considers them a violation of Iraqi sovereignty," it said in a statement.

"It stresses that Iraq is an independent state and that its internal security is its priority. We will not allow it to become a battlefield.

"The Foreign Ministry will summon the Islamic Republic of Iran's ambassador and convey this to him."

ABC/Reuters