By Michael R. Gordon and Ivan Nechepurenko, New York Times–

Long-running tensions between the United States and Russia erupted publicly on Monday as Moscow condemned the American military’s downing of a Syrian warplane and threatened to target aircraft flown by the United States and its allies west of the Euphrates.

The Russians also said they had suspended their use of a hotline that the American and Russian militaries used to avoid collisions of their aircraft in Syrian airspace.

The episode was the first time the United States downed a Syrian plane since the civil war began there in 2011 and came after the SU-22 jet dropped bombs on Sunday near American-backed fighters combating the Islamic State. It followed another major American military action against the Syrian government: a cruise missile strike to punish a nerve gas attack that killed civilians in April.

The latest escalation comes as competing forces converge on ungoverned swaths of Syria amid the country’s six-year civil war. Syrian forces and Iranian-backed militias that support them are extending their reach east closer to American-backed fighters, including forces that the Pentagon hopes will pursue the militants into the Euphrates River valley after they take the Islamic State’s self-declared capital of Raqqa. The collision of the disparate forces has, in effect, created a war within a war.

“The escalation of hostilities among the many factions that are operating in this region doesn’t help anybody,” Sean Spicer, the White House press secretary, told reporters on Monday. President Trump has allowed military commanders more say in conducting operations against the Islamic State, urging them to surround the militants in their strongholds and “annihilate” them.

Russia’s warnings could turn out to be posturing. The Russian military has threatened to halt its use of the hotline in the past — notably after Mr. Trump ordered April’s missile launch — only to continue and even expand its contacts with the United States military. But in the complicated and quickly unfolding situation in Syria, even bluster can risk an unintended showdown.

“Anytime we have multiple armed forces working in the same battle space without de-confliction, there is a dangerous risk of things spinning out of control,” said Douglas E. Lute, a retired three-star Army general who was the United States representative to NATO until January. “Tactical incidents on the ground or in the air over Syria can be misunderstood and lead to miscalculation.”

American military officials rushed to de-escalate the situation, saying they hoped Russia could be persuaded to keep using the hotline.

“This is a delicate couple of hours,” Gen. Joseph F. Dunford Jr., chairman of the Joint Chiefs of Staff, said Monday afternoon. He added that the United States would work both diplomatically and militarily “to re-establish de-confliction.”

But the latest statement from Russia’s Defense Ministry was particularly stark. “All flying objects, including planes and drones of the international coalition, detected west of the Euphrates, will be followed by Russian air defense systems as targets,” said the Defense Ministry statement, which stopped short of declaring that the targets would be shot down.

The Pentagon also vowed to continue airstrikes against the Islamic State in Syria.

The downing of the Syrian SU-22 on Sunday, the first time the American military had shot down an enemy plane since an F-16 took down a Soviet-era MIG-29 during the 1999 conflict over Kosovo, was the latest in a series of confrontations between the United States and forces loyal to President Bashar al-Assad of Syria.

One previously undisclosed confrontation followed a drone attack on June 8 on American-supported Syrians patrolling alongside their coalition advisers. The weapon was a Shahed 129 drone made by Iran, though American officials said they do not know who directed it.

An American F-15E shot down the drone, which had dropped a bomb that missed its target. But a Syrian warplane appeared hours later and began maneuvering to bomb the American-backed fighters, only to be intercepted by an American F/A-18 jet.

“When the airplane got close to where he wanted to deliver his bombs, he realized he had an F/A-18 behind it,” said Lt. Gen. Jeffrey L. Harrigian, who runs the coalition’s air war and described the episode.

Instead of attacking, the Syrian SU-22 zoomed away, and the Americans did not attack.

“We didn’t shoot it because he dumped his bombs off in the middle of the desert,” General Harrigian added in a telephone interview from his command center at Al Udeid Air Base in Qatar.

American officials have repeatedly urged Russians to advise their Syrian allies to keep their distance from the American-supported fighters, known as the Syrian Democratic Forces.

But after a Syrian SU-22 dropped bombs on Sunday near fighters south of Tabqa whom the United States is supporting and advising, an American F/A-18 shot the plane down.

The Russian threat to target American aircraft west of the Euphrates poses complications, particularly because Raqqa, which sits on the river in northern Syria, is well within range of Syrian and Russian air defenses. General Harrigian said there have been “occasional illuminations” or instances when ground-based targeting radars have been directed at coalition planes.

General Harrigan indicated that while the American-led coalition would continue to strike the Islamic State and provide air support for the Syrian Democratic Forces, he had made some adjustments to air operations.

“We have positioned ourselves such that we are able to manage and mitigate threats to our folks to a reasonable level,” he said.

General Harrigian declined to provide details. After the United States cruise missile attack in April, the American-led air war command initially used armed drones in and around Raqqa instead of piloted aircraft, and stealthy F-22s flew around the clock in northeast Syria. This was done to guard against the risk of retaliation by Syrian and Russian air defenses as part of a step-by-step process that eventually saw the United States and its allies return to normal operations.

Weeks after President Vladimir V. Putin of Russia ordered his country’s military forces to Syria in September 2015 to prop up the government of Mr. Assad, Russia and the United States signed a memorandum on preventing air clashes between the two countries.

The hotline has been a crucial link that has allowed Moscow and Washington to notify each other about its air operations over Syria, where Iran, Israel, Russia, Syria, Turkey and the United States with its allies have carried out attacks in pursuit of often-competing aims.

But Moscow has tried to use the agreement as leverage each time the situation has threatened to escalate.

The increasing defiance of American warnings by Iranian-backed Syrian military forces to control eastern Syria comes despite the tough talk from Mr. Trump about pushing back on Iran, Syria specialists said.

“There’s a big strategic game going on,” said Andrew J. Tabler, a Syria expert at the Washington Institute for Near East Policy. “The Iranians are making a play for the Euphrates River valley, and the Russians are going along with it.”

Syrian forces and their partners, for their part, are aiming to take oil-rich Deir al-Zour Province; rescue a Syrian military garrison that is surrounded there; and, many analysts believe, establish a supply corridor that runs from Syria to Iraq and, eventually, to Iran.

Speaking in Beijing on Monday, the Russian foreign minister, Sergey V. Lavrov, seemed to be unaware of the Defense Ministry’s stance that the American attack against Syrian forces was “military aggression.” He called on the United States and all other countries involved in the Syria conflict to “coordinate their actions.”

“We urge everyone to avoid acting unilaterally, to respect the sovereignty of Syria,” Mr. Lavrov said.

“Escalation can never be ruled out,” said Frederic C. Hof, who worked on Syria policy at the State Department under President Obama before leaving and becoming a sharp critic of the administration’s limited support of Syrian rebels. “I doubt, however, that the Russians will permit themselves to be taken hostage by a regime it knows to be both murderous and incompetent.

“But who knows?” Mr. Hof continued. “Common sense and the rational actor model don’t always prevail. One hopes there is a sharp distinction between Russian rhetoric and action.”