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Iran on Wednesday said it had carried out and "concluded" its reprisal over the killing of top Iranian commander Gen. Qassem Soleimani when it targeted US forces in Iraq with missile strikes.

"Iran took and concluded proportionate measures in self-defence" targeting a base from which a "cowardly armed attack against our citizens and senior officials" was launched, said Foreign Minister Mohammad Javad Zarif on Twitter.

"We do not seek escalation or war, but will defend ourselves against any aggression."

The missile strikes hit the Ain al-Asad air base in western Iraq and a base in Erbil, where US and other foreign troops were deployed as part of a coalition fighting the Islamic State (IS) extremist group.

This was the first time that forces in Iran directly targeted US troops, instead of using proxy militias. Soleimani was killed in a US airstrike on Friday 3 January. No US casualties were reported in the bombing.

Soleimani led the Quds Force, the extraterritorial branch of the Islamic Revolutionary Guards Corps (IRGC), and had been involved in the creation of the Iraqi Popular Mobilisation Forces (PMF) militias as well as militias which propped up Bashar al-Assad’s regime in Syria.

Iran's supreme leader Ayatollah Ali Khamenei said a "slap in the face" had been delivered to the US but in contrast to Zarif, hinted that more actions could be taken

"An important incident has happened. The question of revenge is another issue," Khamenei said in a speech broadcast live on state television.

"Military actions in this form are not sufficient for that issue. "What is important is that America's corrupt presence must come to an end in this region," he added.

The office of Iraqi Prime Minister Adel Abdel Mahdi said that Iran had informed it of the strikes. Iraqi President Barham Saleh denounced the bombing as a violation of Iraq’s "state sovereignty".