All members of the Atlantic alliance stood behind the United States in the Middle East after it briefed NATO on its drone attack that killed Iranian military commander Qassem Soleimani, NATO Secretary-General Jens Stoltenberg said on Monday.

Speaking after a rare NATO meeting on Iran and Iraq in which the United States briefed its allies about last Friday's drone attack, Stoltenberg also called for a de-escalation of tensions, echoing the statements of some European leaders.

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"We are united in condemning Iran's support of a variety of different terrorist groups," Stoltenberg said. "At the meeting today, allies called for restraint and de-escalation. A new conflict would be in no one's interest. So, Iran must refrain from further violence and provocations."

Despite anger last year among European NATO allies over US strategy in the Middle East under President Donald Trump, two diplomats present confirmed that the two-hour meeting at NATO headquarters went smoothly.

They said that no envoy challenged US State Department and Department of Defense officials, who briefed via video conference, over the merits of Friday's drone raid.

There was also no discussion or criticism of Trump's list of targets, that include cultural sites, if Iran were to retaliate with attacks on Americans or US assets, the diplomats said.

The meeting, which took place on a day of a huge outpouring of national grief for Soleimani in Iran, centred mainly on NATO's decision to suspend its training mission in Iraq, after an Iraqi parliamentary resolution called on foreign troops to leave.

While there was concern that the killing of Iran's second-most powerful man could trigger a conflagration in the Middle East, France, Germany and others said they wanted the Iraq mission to continue.

"It would send the wrong signal if we withdraw," one NATO diplomat said.

The NATO Iraq mission, made up of several hundred trainers, advisers and support staff from both countries of the 29-member alliance and non-NATO partner countries, includes military and civilian personnel.

Established in Baghdad in October 2018 after three years of war against ISIL (ISIS) fighters, the mission is a non-combat "train-and-advise" mission to help Iraqi security structures and institutions fend off future insurgencies. Its personnel do not deploy with Iraqi forces during operations.

"It's still not clear what will happen with NATO's mission in Iraq," said Al Jazeera's Natacha Butler, reporting from Brussels.

"NATO forces ... suspended training operations for security reasons on Saturday. Iraqi lawmakers have requested foreign troops to leave the country."