“The tank had been maneuvering with coordinated indirect fire on a defensive position occupied by Syrian Democratic Forces and coalition advisers,” Colonel Dillon said. “The defensive position was within effective range of the hostile weapons systems.” Coalition officials had maintained regular contact with their Russian counterparts, he said, to avoid dangerous misperceptions or miscalculations.
The Kremlin — seeking to play down its involvement in the fighting in Syria and seemingly hoping to avoid escalating tensions with the United States — has sidestepped questions about the episode.
It has stressed repeatedly since last Wednesday that no members of the Russian armed forces were killed, and that any Russians fighting alongside the Syrians were mercenaries.
“We only handle the data that concerns Russian forces servicemen,” Dmitri S. Peskov, the Kremlin spokesman, said at a news briefing on Tuesday. “We don’t have data about other Russians who could be in Syria.”
The Kremlin said much the same about the nature of the fighters in Crimea and eastern Ukraine in 2014, claiming they were volunteers and men on vacation, only to admit later that they were regular soldiers.
President Vladimir V. Putin of Russia has said at least three times since 2016 that combat operations in Syria were winding down, including once during a surprise visit to a Russian air base in Syria last December. Yet there are hundreds if not thousands of contract soldiers in Syria whom the Russian government has never acknowledged.
They were deployed both to help keep the official cost down and to avoid the kind of reports that emerged from Russia’s intervention in Afghanistan in the 1980s, which became unpopular with ordinary Russians as the toll of young soldiers rose. Even though the Kremlin changed the law during Ukraine crisis in 2015 to make battlefield casualties a secret, the funerals for regular soldiers killed in combat need to be more official than those for mercenaries.
Also, even if Mr. Putin made Russia a player in the Middle East by sending his miliary into Syria in September 2015, the intervention has never been particularly popular at home. Mr. Putin, running a re-election campaign that he is sure to win, has sought to take the spotlight away from overseas issues and to stress that his main concerns are domestic.
But individual Russians have begun speaking out. Some announced the specific names of victims, and others claimed that “scores” of Russian fighters had died in an American airstrike near Deir al-Zour, between the Euphrates River and the Iraqi border.
Aleksandr Ionov, a Russian businessman working in Syria offering security and other services, said his associates in several private military organizations said that there had been heavy losses, estimating that more than 200 might have been killed.
Aleksandr Averin, a member of the Other Russia nationalist party, confirmed that Kirill Ananiev, a party member who left for Syria about a year ago, was killed in the airstrike, noting that there were other “substantial losses.”
Mr. Ionov said not all those killed were Russian: Some of the paid fighters came from other countries that were once part of the Soviet Union. “More than 200 is the current estimate. We cannot know the exact number yet, but most of them were Russian,” he said in a telephone interview.
Mr. Ionov said he was speaking out, like a growing number of opposition and other voices, because he wanted the Russians who were killed to be officially recognized for their sacrifice.
“The truth has to be told,” he said. “If people died, then this should be recognized and respects should be paid to people who fought against terrorists.”
He called on the government to give a fuller version of events, adding, “People are outraged because they want to know the truth.”
What exactly sparked the battle also remains unclear. Some reports suggested that the fight was over control of a gas field. Mr. Ionov said he believed that it was caused by the fog of battle, with the American-backed Kurdish troops interpreting the movement of government ground forces as an attack to control an oil field and calling in an airstrike.
The Kremlin continues to sidestep the questions.
Other sources like Mr. Averin have also suggested that many Russians died.
“I can confirm that Kirill died on Feb. 7 in Syria, near the Euphrates River, as a result of a strike by the American coalition,” Mr. Averin said in an interview, adding that he was aware of “substantial losses” suffered by “paramilitary structures with ties to Russia.” He did not elaborate.
Another victim, Vladimir N. Loginov, died “in an unequal fight on Feb. 7 in the area of Syria’s Deir al-Zour,” according to a statement published online by his paramilitary organization.
“He died, heroically defending our motherland in the far reaches against the invasion of maddened barbarians,” the Baltic Cossack Union in Kaliningrad said in the statement.
Mr. Loginov, 51, had been a member of the local Cossack group, a pro-government paramilitary organization, since 2014.
In another case, Lubava Kocheva, a woman from central Russia, said in a brief online chat that two of her male friends in Syria, Igor Kosoturov and Stanislav Matveev, also died on Feb. 7.
“We don’t know anything, whether they will bring them or not,” said Mrs. Kocheva, 41, referring to the men’s corpses. “This is very difficult and frightening.”
The names of most of the victims identified so far were first reported by the Conflict Intelligence Team, a group of Russian investigative bloggers. The exact circumstances of their deaths could not be established by The New York Times.
The Russian Defense Ministry, which supports President Bashar al-Assad of Syria in the ongoing civil war, said none of its servicemen had been involved in the clash and that only 25 pro-government Syrian insurgents were wounded. It took pains to distance itself from the battle.
“The reason for the incident was lack of coordination between the reconnaissance movements of the Syrian insurgents and the Russian operative command,” the ministry said in its statement on Thursday.
The number and exact nature of private Russian security firms operating in Syria is unclear, although there have been persistent reports in the Russian news media that some militiamen who fought on the side of the Russian-backed separatists the war in eastern Ukraine were later deployed to Syria.
The main attention has focused on the so-called Wagner Group, a paramilitary organization known by the nickname of the retired Russian officer who leads it. The organization, whose relationship with the Kremlin is murky and unconfirmed, has been operating in Syria in various capacities, including protecting some oil fields, according to multiple reports by the Russian news media. Its leaders have reportedly received awards in the Kremlin and its mercenaries are trained at the Russian Defense Ministry’s facilities.
Grigory A. Yavlinsky, a veteran Russian opposition politician who is a candidate in next month’s presidential election, called on Mr. Putin to disclose the number of Russians who had died in Syria.
“I demand an explanation as to why Russian nationals take part in ground military operations in Syria, despite the statements by the president and defense minister that Russian military formations will be withdrawn from this country,” Mr. Yavlinsky said in a statement. “I also think there needs to be a public report about relations with the U.S., as there is a growing threat of an accidental or deliberate direct military clash between Russia and America.”
The official Kremlin stance is that its military deployment in Syria is now centered on two permanent bases, one for Russia’s air force and one for its navy, there by invitation from the Syrian government.
Russian political analysts said that the country’s reluctance to confirm that its citizens had died as a result of a United States-led airstrike was actually a sign that Moscow did not want to further worsen the already fractured bilateral relations with Washington.
“This is a very rare case, where the positions of Russia and the U.S. got closer,” said Aleksei V. Makarkin, an analyst at the Center for Political Technologies, a think tank in Moscow. “No one wants to take steps that will do irreparable damage to the already broken Russia-U.S. relations.”