Originally appeared in The Wall Street Journal

Russian reconnaissance flights over Iraq to spy on Islamic State militants would complicate the U.S.-led campaign against the extremist group but wouldn’t obstruct it, American officials said Monday after Baghdad left open the possibility of overflights by Moscow.

At the same time, U.S. ability to share intelligence with Iraq could be diminished if the Iraqis are sharing information with the Russians, American defense officials said.

An Iraqi defense ministry spokesman said Monday that his country would be open to Russian intelligence gathering in Iraqi airspace.

The comments came a day after Iraq said it had reached an intelligence-sharing agreement with Russia, the Syrian regime and Iran.

“If Russia needs to participate in aircraft reconnaissance flights, it can make a formal request to the Iraqi government and there will be no objection in my opinion,” said the spokesman, Brig. Gen. Tahseen Ibrahim.

The developments of the past few days signaled a deepening military role for Moscow in Iraq in the midst of a Russian military building in neighboring Syria to prop up President Bashar al-Assad.

Russian officials say “specialists” are on the ground in Syria to help train and equip the president’s forces.

American officials were still trying to decipher Russia’s motives in Iraq and Syria—both of which have lost significant territory to Islamic State.

Russian President Vladimir Putin and U.S. President Barack Obama met Monday on the sidelines of a United Nations summit. A senior administration official said Mr. Obama came away believing Russia’s intentions in Syria are to fight Islamic State.

The two leaders agreed the U.S. and Russian militaries will hold discussions on how to avoid coming into conflict with each other as they both fight Islamic State, the official said.

“It does add a degree of complexity to our operations,” Col. Steve Warren, an American military spokesman in Baghdad, said of the possibility of Russian reconnaissance flights over Iraq. “But it doesn’t cause us to have to stop,” he said of U.S.-led airstrikes on Islamic State—also known as ISIS or ISIL.

Mr. Putin ruled out sending large number of ground troops into Syria.

Col. Warren said he had no indications that the Iraqis had reached out to the Russians for help.

“I think that it is the Russians reaching out to the Iraqis,” he said. Iraq is already well-served by information from U.S. reconnaissance, Col. Warren added.

Iraq is already well-served by information from U.S. reconnaissance, Col. Warren added.

Though Russia has long exercised considerable influence in Syria, it has yet to get involved in Iraq where the U.S. has been active in supporting Iraqis fighting Islamic State.

Senior Obama administration officials said they expect Iraq could share intelligence from the U.S. with Russia, and therefore Syria, and now has to factor that into cooperation with Baghdad. Col. Warren said the U.S. and Iraqis currently share only intelligence that is specific to Islamic State targets in Iraq. The U.S. “always takes appropriate precautions to safeguard sources and methods,” he said.

Defense officials said the U.S. already must take care to ensure that intelligence shared with the Iraqis doesn’t wind up in the hands of Iran—a close ally of both the Syrian regime and the Shiite-led Iraqi government. Similar restrictions could help mitigate the risk of Iraq sharing U.S. intelligence with the Russians and the Syrians, officials said.

Officials said, however, that it wouldn’t significantly change the U.S. approach to the fight against Islamic State, in part because much of the process for intelligence collection for the effort isn’t highly sensitive. U.S. officials stressed Iraq is a sovereign country, and Washington can’t block the government from cutting a deal with Russia.

“We know many nations in the region—like Iran—have significant interests in ISIL’s defeat,” a senior administration official said.

“Our message to them has been consistent: Whatever unilateral actions they take should not interfere with coalition operations.”

The Iraqi government said the intelligence-sharing pact would set up a committee to coordinate the efforts between the four countries.

But it remained unclear whether that committee would coordinate with other nations—particularly rivals such as the U.S.—and if so, how.

Mr. Putin said Russia was setting up a center with Iraq, Syria and Iran to “coordinate the efforts of regional powers in fighting” Islamic State and other terrorist groups. He said Russia was open to any other countries joining.

“It’s not about having a unified command…but at least coordinating our actions.”