Jordan's flag carrier Royal Jordanian issued a statement saying it had "decided to halt its services between Amman and Baghdad... until further notice, in light of the security situation in the city and at Baghdad International Airport".

The airline operates 18 flights per week between Amman and Baghdad, the statement said, adding that routes to other Iraqi cities have not been effected.

Bahrain's Gulf Air also suspended flights to and from Baghdad and the shrine city of Najaf south of the capital until further notice "due to safety and security issues", the carrier announced on Twitter.

The United States carried out an air strike that killed top Iranian commander Qasem Soleimani and nine others, including members of an Iraqi pro-Iranian group, outside Baghdad's airport early Friday.

The strike sparked fears of an escalation in violence in the region, with Iran vowing "severe revenge" for Soleimani's death.

Royal Jordanian and Gulf Air are the only two carriers to confirm flight suspensions so far, but others said they are monitoring the situation.

A Qatar Airways spokesman said the airline was still flying to Baghdad "with caution".

"If any slight change we may cancel -- slight change meaning escalation," he said.