In recent weeks, Russian bombers have intensified airstrikes against Islamic State militants in eastern Syria. There have been reports that the Russians have met with Syrian Kurdish fighters — the backbone of the American-supported militia battling the Islamic State — with offers of military assistance.
President Vladimir V. Putin of Russia declared on Wednesday that the Islamic State in eastern Syria had suffered a “complete defeat” — a boast that American officials said exaggerated Moscow’s role and seemed to ignore the contentious efforts to rout the remaining 3,000 Islamic State disciples still on the run.
Russian officials did not respond to an email seeking comment.
Russia and the United States back separate offensives against the Islamic State, also called ISIS, in eastern Syria, both of which are advancing in oil-rich Deir al-Zour Province bordering Iraq. The assaults are converging on Islamic State holdouts from opposite sides of the Euphrates, which bisects the province. Syrian Army troops backed by Russian air power and Iranian militia are advancing along the western side of the river; Syrian Arab and Kurdish fighters, supported by American warplanes and Special Operations advisers, are pushing along the eastern river banks.
The shrinking physical distance between the two forces has raised the risk of inadvertent clashes, a problem that Russia and the United States have tried — at least in principle, if not always practice — to avoid.
Two years ago, the Russian and American militaries established a special hotline to help prevent disasters in the air. Every day, an American Air Force officer calls his Russian counterpart at an air base in Latakia, Syria, to head off, or “deconflict,” as the military says, any potential problems over Syria.
Several months ago, a regular call was started between a Russian officer and an American officer at a command center in Kuwait to deconflict ground movements in eastern Syria.
Gen. Joseph F. Dunford Jr., the chairman of the Joint Chiefs of Staff, has spoken to Gen. Valery V. Gerasimov, the chief of the Russian general staff, about a dozen times in the past year, most recently on Wednesday, “to avoid miscalculation and to promote transparency in areas where our militaries are operating in close proximity,” said General Dunford’s spokesman, Col. Patrick Ryder.
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The daily phone calls between the air bosses have remained professional, but the dialogue does not always reflect what American commanders in the region see in the skies, prompting as many as a dozen additional calls a day from the Americans demanding explanations for Russian violations.
“We’ve had contentious calls,” said Col. Jeff Hogan, deputy commander of the air operations center at the Qatar base, who speaks to his Russian counterpart daily through a translator. “The Russians have a vote in Syria, and sometimes people forget that.”
In early November, as the airspace constricted over the shrinking battlefield, the two sides agreed to the Euphrates as the dividing line for operations. If either military needed to cross the river for any reason, the agreement was to call ahead first.
That did not happen on Nov. 15, when the two A-10s dodged the Russian Fencer. Nor did it happen the next two days, Nov. 16 and Nov. 17, when a Russian Su-30 Flanker flew 1,000 feet directly below A-10s, both times crossing into airspace east of the Euphrates River.
On Nov. 17, two American F-22 Raptors encountered an armed Russian Su-24 Fencer that had crossed into the airspace east of the Euphrates, and made three passes directly over allied ground forces for 20 minutes.
During that time, the F-22 pilots attempted to contact the Fencer five times by radio with no response or reaction. The Air Force pilots showed restraint, but given that the actions of the Su-24 could have reasonably been interpreted as threatening to the American aircraft, the F-22 pilots would have been with their rights to fire in self-defense, officials at the Qatar air base said.
A flurry of phone calls between the two sides temporarily eased tensions, with the Russians claiming some violations were brief overflights to allow them safer flight paths to strike ISIS targets on the side of the river. Still, the violations have continued.
“It’s become increasingly tough for our pilots to discern whether Russian pilots are deliberately testing or baiting us into reacting, or if these are just honest mistakes,” said Lt. Col. Damien Pickart, the command’s spokesman. “The greatest concern is that we could shoot down a Russian aircraft because its actions are seen as a threat to our air or ground forces.”
The setting was similar last June in southern Syria, when American warplanes shot down a Syrian Air Force Su-22 and two Iranian-made drones after they had threatened American-backed militia forces.
The risky flying behavior of the Russians has complicated the American hunt for the remaining Islamic State fighters in a pocket near the border with Iraq, forcing General Harrigian to pull some fighter jets off attack missions to protect unarmed surveillance planes hovering over the 15-square mile piece of ISIS-controlled territory.
General Harrigian said only one main enemy lurks in the deserts of eastern Syria. “We’re all here killing ISIS,” he said. “We’re not here to fight the Russians.”
An earlier version of a picture caption with this article misstated the type of plane pictured. It is a bomber, not a fighter jet.