Iranian state television said Iran had fired 15 missiles at US targets, a response to Friday's killing of Qassem Soleimani. The US military said at least two Iraqi facilities hosting US-led coalition personnel were targeted.
China urged the United States and Iran to exercise restraint and resolve their dispute via dialogue.
"The worsening of the situation in the Middle East region is not in any side's interests," Chinese foreign ministry spokesman Geng Shuang said during a daily briefing on Wednesday, reiterating a call for a peaceful resolution of the conflict.
Iran missile attacks target US forces in Iraq
China has criticised the United States for aggravating tension in the Middle East through its use of force in the standoff between Washington and Tehran.
An editorial on Tuesday in the government-run China Daily blamed the US for creating a "cauldron of tensions" in the region.
Asked on Wednesday what China was doing to help resolve the conflict, Geng told reporters China is in close contact with relevant parties in the United Nations Security Council.
France in a similar way said de-escalation was priority after Iran strikes on US forces.
"The priority is more than ever for a de-escalation," Foreign Minister Jean-Yves Le Drian said in a statement. "France remains determined to work to ease tensions and is in contact with all the parties to encourage restraint and responsibility," he added.
Iran supreme leader says 'slap in face' delivered to US
Britain condemned the Iranian missile attack and urged Tehran no to repeat the ‘reckless and dangerous attacks’.
"We urge Iran not to repeat these reckless and dangerous attacks, and instead to pursue urgent de-escalation," British Foreign Secretary Dominic Raab said.
Meanwhile, Turkey's foreign minister will visit Iraq on Thursday to try to ease tensions.
Foreign Minister Mevlut Cavusoglu will travel to Iraq as part of Ankara's "intensified diplomatic efforts to alleviate the escalated tension in the aftermath of recent developments in the region", the ministry said in a statement.
Cavusoglu also spoke to Iranian Foreign Minister Javad Zarif by phone, it said in a separate statement.
Cavusoglu said on Monday that Turkey was in contact with all parties in the region and Washington to de-escalate tensions, adding that Ankara would work to help solve the issue.
Germany's defence minister called on Tehran to end a ‘spiral’ of conflict.
"The German government strongly condemns this aggression," Annegret Kramp-Karrenbauer told broadcaster ARD.
"It is now crucial that we do not allow this spiral to continue," said the defence minister, adding that "it is now primarily up to the Iranians to refrain from further escalation."
Kramp-Karrenbauer said that Germany had been in contact with the US department of defence throughout Tuesday night, and that "all channels" of communication would be opened in a bid to prevent further escalation.
She added that she would seek a meeting of the coalition's 13 framework nations to discuss the situation in the region.
Separately, Foreign Minister Heiko Maas urged Iran to "refrain from all steps that could lead to further escalation". He also called on all parties to excercise restraint.
The overnight attack on bases in Al-Asad and Arbil was the latest escalation amid growing tensions in the region since a US drone strike killed Iranian general Qassem Soleimani last Friday.
The EU's diplomatic chief also urged an end to the "spiral of violence".
"The latest rocket attacks on air bases in Iraq used by US and coalition forces, among them European forces, are yet another example of escalation and increased confrontation," Josep Borrell told reporters.
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