BAGHDAD - Iraq will send delegations to the U.S. and Iran to help end tensions between the two countries, Prime Minister Adel Abdul-Mahdi said Tuesday, adding that Baghdad is neutral in the conflict.

Abdul-Mahdi, whose country has close ties to both Iran and the U.S., said that Iranian and U.S. officials have informed Iraq that they have “no desire in fighting a war.”

Last week, the U.S. ordered the evacuation of nonessential diplomatic staff from Iraq amid unspecified threats from Iran and rising tensions across the region. The White House has sent warships and bombers to the region to counter the alleged Iranian threats.

Abdul-Mahdi’s comments came two days after a rocket slammed into Baghdad’s heavily fortified Green Zone, landing less than a mile from the sprawling U.S. Embassy. No injuries were reported and no group immediately claimed the Sunday night attack.

Major Iranian-backed groups in Iraq distanced themselves from the attack saying their country should not be pulled into regional conflict.

After America’s 2003 invasion of Iraq to oust dictator Saddam Hussein, American troops and Iranian-backed militiamen fought pitched battles around the country, and scores of U.S. troops were killed or wounded by sophisticated Iranian-made weapons.

Abdul-Mahdi said Iraq is “playing a role to calm the situation but it is not a mediation.” He said he will visit Kuwait on Wednesday to discuss regional issues.

“Iraq is only carrying messages (between the U.S. and Iran). Mediation is a big word. What we are doing is trying to defuse the crisis,” he told reporters in Baghdad during his weekly news conference, without going into details about the delegations that will be sent. “We are transferring messages from one side to the other.”

“Iraq has no choice in the crisis. We don’t stand by one side against the other,” Abdul-Mahdi added.

On May 8, U.S. Secretary of State Mike Pompeo made a lightning, previously unannounced trip to the Iraqi capital following the abrupt cancellation of a visit to Germany, and as the United States said it had been picking up intelligence that Iran is threatening American interests in the Middle East.

Abdul-Mahdi was asked whether Iraq is taking any measures in case the Strait of Hormuz, the narrow mouth of the Persian Gulf through which a third of all oil traded at sea passes, is closed. Most of Iraq’s oil exports pass through Hormuz.

“We are working for alternatives but these are not short-term alternatives. They are long-term ones,” he said.

“We have stored fuel for the crisis” in the local market in case something happens, he said.