Smoke billows following a reported strike by Syrian government forces in a rebel-held neighborhood in the northern city of Aleppo on Tuesday. (Karam Al-Masri/AFP/Getty Images)

The Obama administration’s offer to coordinate air attacks in Syria with Russia has opened a deepening rift between senior national security officials who insist it could quiet Syria’s civil carnage and further larger counterterrorism goals, and those who consider it a counterproductive sellout to the Kremlin.

Secretary of State John F. Kerry, who said last month that reaching an “understanding” with Russia was “the most important thing” in moving Syria forward, plans to push the deal when he meets Thursday in Moscow with President Vladi­mir Putin.

The U.S. proposal, which has not been made public, calls for the establishment of a “Joint Implementation Group” with Russia, through which the two countries would initially exchange intelligence and operational information on the locations of Jabhat al-Nusra, al-Qaeda’s Syrian affiliate, and “synchronize” their independent operations against the Islamic State. Once al-Nusra targets have been agreed, they would determine what action to take and “deconflict” their air operations.

In exchange, Moscow would use its leverage to effectively ground Syria’s air force, limiting its operations to non-combat humanitarian and medical-evacuation missions. Both the United States and Russia would recommit themselves to pushing for a political settlement to Syria’s civil war.

Kerry is “extremely frustrated,” State Department spokesman John Kirby said. “And that’s one of the reasons why we’re going to Moscow, to see if that change is actually going to be possible — if the Russians are going to do what they’ve said they were going to do.” Administration officials have declined to discuss details of the proposal.

People walk on the rubble of a site hit by a barrel bomb in the rebel held area of Old Aleppo on Monday. (Abdalrhman Ismail/Reuters)

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Despite a cease-fire ostensibly in effect since February, Syrian planes have kept up a steady bombardment of both civilian and opposition sites — where they have argued that al-Nusra forces, exempt from the truce, are mixed with rebel groups covered by the accord. After observing the early weeks of the cease-fire, Russian planes joined the Syrian forces, including in an offensive last weekend that took over the only remaining supply route for both rebels and civilians hunkered down in the northern city of Aleppo.

After days of air bombardment riddled an area only a few miles wide, Syrian forces and allied militiamen from Iraq, Iran and Lebanon’s Hezbollah militant group took up positions above what is known as the Castello Road leading to Turkey. Artillery, rockets and surface-to-surface missiles have struck dozens of passenger cars and minibuses that attempted to drive the route, rebel spokesmen said. The area is so dangerous, they said, they have been unable to retrieve scores of bodies still trapped in the destroyed vehicles.

On Monday, rebel forces shelled government-held areas of the city, killing scores of residents, according to Syrian state media.

With government forces now virtually surrounding the city, the United Nations on Tuesday expressed concern about a prolonged siege. U.N. officials estimated that 300,000 civilians stuck inside the area would be cut off from dwindling supplies of food and medical care, as well as from their only escape route.

A new coordination agreement with Moscow, supporters within the administration argue, would save lives by stopping air attacks on civilians and opposition fighters, while simultaneously increasing the focus on al-Nusra, a shared U.S.-Russian enemy. Al-Nusra forces are amassed south of Aleppo, but their scattered presence among rebel fighters to the north has been used as an excuse for both Syrian government and Russian attacks.

But as Kerry and Robert Malley, the chief White House point man on Syria, negotiate with the Kremlin, a growing chorus of defense, diplomatic and intelligence officials have voiced objections.

“We do this, and then what?” said a U.S. official, one of several who spoke on the condition of anonymity because they were not authorized to discuss the issue and feared identification as internal critics.

“You need to solve the Assad problem, because as long as Assad is in power, Syria is a failed state. And as long as it’s a failed state, it will be a breeding ground for extremists,” including the Islamic State and al-Nusra, the official said.

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This official and others, in comments that were echoed across a wide range of outside Syria experts, said that the proposed deal does not appear to affect Syrian or Russian ground operations — including extensive Russian artillery being used in the Aleppo offensive — and does nothing to force Assad to negotiate a political end to the war, something both he and Russia agreed to as part of the original cease-fire arrangement.

“I don’t understand how Kerry walks away from this saying he got something,” said Andrew J. Tabler of the Washington Institute for Near East Policy. “It’s all in the name of saying . . . that they’re saving lives and targeting terrorists. But what it will do strategically will mean the regime will simply stand by while we hit the terrorists, and the regime will benefit from that.”

“This is defeat,” Tabler said. “I think everybody is beside themselves because this is all being done in the name of a cease-fire . . . the best thing we can do to reduce the violence. But in effect, it’s crafted in such a way that it strengthens the regime, the opposite of what we say we want.”

Frederic C. Hof of the Atlantic Council, who served as the administration’s special adviser for Syria until resigning in late 2012, advised the administration to “take a deep breath and think things through very carefully.”

“As desirable as it is to damage a loathsome al-Qaeda entity, military collaboration with Russia could also exact long-term costs to America’s reputation and the broader fight against extremism, costs potentially far exceeding the benefits of a here-and-now body count,” Hof wrote in the Huffington Post on Tuesday.

Internal disagreement over Syria policy has plagued the administration for years. In 2012, then-Secretary of State Hillary Clinton argued for the use of military force against Assad and for the establishment of opposition safe zones. In addition, then-CIA Director David H. Petraeus recommended arming and training anti-Assad opposition forces.

President Obama rejected both proposals and, to the consternation of most of his national security cabinet, pulled back in 2013 from an agreed plan to bomb Syrian military targets to punish Assad for the use of chemical weapons.

Among the many arguments against the currently proposed deal with Russia, the Pentagon has insisted that Moscow has demonstrated — in Syria, Ukraine and elsewhere — that it simply cannot be trusted.

The stated purpose of airstrikes that Russia began last fall was “to fight ISIL and . . . assist the political transition in Syria towards a post-Assad government,” Defense Secretary Ashton B. Carter said late last month. “They haven’t done either of those things.”

ISIL, along with ISIS and Daesh, is an alternative term for the Islamic State.

While Kerry has long advocated for U.S. military action against Assad, he believes that the highest priority now must be to stop the violence generated by Syrian government airstrikes. He feels that any downside to cooperation with Russia would be mitigated by the pressure Moscow could bring on Assad and gains against an al-Nusra organization that remains a vital component of al-Qaeda’s international operations.

Hugh Naylor in Beirut contributed to this report.