WASHINGTON >> The U.S. and Russia on Tuesday put into practice new rules designed to minimize the risk of air collisions between military aircraft over Syria, while Iraqi leaders pledged they would not invite Russian airpower over their nation.

Marine Gen. Joseph Dunford, chairman of the Joint Chiefs of Staff, said the Iraqis promised they will not request any Russian airstrikes or support for the fight against Islamic State militants.

Shortly after leaving Baghdad, Dunford told reporters traveling with him that he laid out a choice when he met with Iraqi Prime Minister Haider al-Abadi and Defense Minister Khaled al-Obeidi earlier Tuesday.

"I said it would make it very difficult for us to be able to provide the kind of support you need if the Russians were here conducting operations as well," Dunford said. "We can’t conduct operations if the Russians were operating in Iraq right now."

He said there was "angst" in the U.S. when reports surfaced that al-Abadi had said he would welcome Russian airstrikes in Iraq. The U.S., Dunford said, "can’t have a relationship right now with Russia in the context of Iraq."

Meanwhile, Washington and Moscow reached agreement on the rules for aircraft over Syria. A Russian defense official in Moscow said the "memorandum of understanding" suggests a potential for U.S.-Russian counterterrorism cooperation, but U.S. officials said it was a narrow arrangement that does not lessen Washington’s concern about the Russian military campaign.

There is no plan to establish zones of cooperation in the parallel air campaigns or to share intelligence or target information in Syria, Pentagon spokesman Peter Cook said.

The Pentagon has cited several instances when Russian aircraft came too close to U.S. warplanes over Syria in recent weeks. More broadly, Washington has complained that instead of hitting Islamic State fighters, Russian airstrikes are mostly targeting rebel forces fighting the Syrian government. Russia also deployed ground troops and land-based weaponry, including multiple-launch rocket systems, in support of the Syrian government.

The arrangement announced Tuesday "does nothing to assuage our concerns about Russian military activities in Syria," State Department spokesman John Kirby said.

Cook said Gen. Lloyd Austin, commander of U.S. Central Command, signed for the U.S. side Tuesday. At a Pentagon news conference, Cook gave a broad description of the document but said the U.S. had accepted a Russian request that the text be kept secret.

After several rounds of talks that began more than a week ago, the two sides agreed to a number of air safety protocols including "maintaining professional airmanship" and the use of specific aircraft communications frequencies, Cook said. They agreed to keep a "safe distance" between aircraft, Cook said, but he would not say whether specific distances were written into the memo.

The two sides also agreed to establish a "communication line on the ground" as a backup of military-to-military communication, Cook said, although he would not say whether this would be a telephone line or where it would be located. A U.S.-Russia working group will be formed to deal with any implementation issues that arise, he added.

The discussions that led to the protocols "do not constitute U.S. cooperation or support for Russia’s policy and actions in Syria," Cook said. "In fact, far from it, we continue to believe that Russia’s strategy in Syria is counterproductive, and their support for the Assad regime will only make Syria’s civil war worse." He was referring to Syrian President Bashar Assad, whom the U.S. says is an illegitimate leader and must leave office.

The U.S. has been bombing Islamic State targets in Syria since September 2014; the Russian air campaign began less than one month ago.

In Moscow, Russian Deputy Defense Minister Anatoly Antonov said in a statement carried by Russian news agencies that signing the memorandum was a positive step that has "important practical meaning."

"The memorandum contains a complex of rules and restrictions aimed at preventing incidents between Russian and U.S. aircraft," Antonov said, adding that Russian and U.S. military officials will set up round-the-clock communications channels and "determine the mechanism of interaction, including mutual assistance in crisis situations."

"The Americans have promised to get the agreed rules to all participants of the anti-IS coalition they lead, so that their pilots proceed from those agreements," he said, referring to the U.S. coalition that includes Australia, Bahrain, Canada, France, Jordan, Saudi Arabia, Turkey and the United Arab Emirates.

Antonov added that the memorandum "shows a big potential for cooperation between Russia and the U.S., including in the fight against terrorism, which we are ready to expand and deepen."

In Iraq, Dunford visited with Kurdish leaders and commanders in the northern city of Irbil and then flew to Baghdad to meet with the ministers and U.S. military leadership.

Dunford said the Iraqis’ response was encouraging, adding that he told the ministers he would be reporting that answer to U.S. leaders when he gets home.

"A key part of our report going back is that both the prime minister and the defense minister said that they recognize that the partnership and the relationship" with the U.S.-led coalition was the critical relationship they needed in order to deal with a common threat.

Dunford also said Iraqi leaders told him that the planned intelligence coordination center operated by the Russians and Iranians in Baghdad hadn’t done anything yet. But they also noted that the Iraqi military uses a lot of Russian-made equipment, and Dunford said it is reasonable for them to get parts and support for that gear.

Baldor reported from Baghdad. Associated Press writer Vladimir Isachenkov in Moscow contributed to this report.