US President Donald Trump, while delivering a televised address on Wednesday in response to Iran's missile attacks, announced more "punishing" economic sanctions even as he extended an olive branch to the "people and leaders" of Iran to work together for "shared priorities".

Iran launched strikes on two US military bases in Iraq in response to the killing of top Iranian general Qasem Soleimani in a US drone strike last week.

Trump defended the targeted killing of Gen. Soleimani, the head of Iran's elite Quds Force. He added that Americans should be extremely grateful and happy with the outcome.

He announced that the US “will immediately impose additional punishing economic sanctions on the Iranian regime” in response to what he called “Iranian aggression”.

Experts have viewed Iran's move as a measured response, saying that it had deliberately avoided US military casualties to prevent the crisis from escalating out of control while still signalling Iranian resolve.

Trump confirmed no Americans were harmed in the Iranian attacks and suggested Washington might not carry out immediate retaliation, a sharp contrast to his earlier statements threatening military retaliation and strikes at '52 Iranian locations'.

Know more: Trump vows to hit 52 Iranian targets if Iran retaliates after drone strike*

“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.

The US president acknowledged Iran "appears to be standing down" at the moment "which is a good thing for all parties concerned and a very good thing for the world".

The much-awaited address, which began almost half an hour after its scheduled time, began with Trump saying, "As long as I am president, Iran will not be allowed to hold nuclear weapons."

At the end of the almost nine-minute-long speech, Trump signalled to Iran that the US would be willing to work with it toward a "better future".

“To the people and leaders of Iran, we want you to have a future and a great future, one that you deserve,” Trump said. “One of prosperity at home and harmony with the nations of the world.”

Flanked by US Vice President Mark Pence, US Secretary of State Mike Pompeo as well as several military officials, Trump called for new nuclear negotiations to replace the 2015 nuclear deal from which he withdrew the US.

Trump also announced he would ask NATO to become “much more involved" in the Middle East process.

Iraq’s military said 22 missiles were launched on the Ain al-Asad air base in western Anbar province and a base in the Iraqi Kurdish capital Erbil, causing no casualties among Iraqi forces.

Following the attack, the international community had sounded alarm and concern, urging both sides to de-escalate.

Trump had announced he would make a statement in the morning as an assessment of casualties and damage after the late-night attack was underway.

"All is well!" Trump said in the Twitter post. "So far, so good! We have the most powerful and well equipped military anywhere in the world, by far!"