Secretary of State John F. Kerry said he plans to meet with his Russian counterpart later this week for further talks on a proposal for the rebels’ departure from Aleppo that was first discussed Friday. (Francois Lenoir/Reuters)

The United States is discussing with Syrian rebels their surrender and evacuation from Aleppo, as Russia on Tuesday threatened the imminent “elimination” of anyone who refuses to leave the city.

“Those who refuse to leave of their own accord will be wiped out,” Russian Foreign Minister Sergei Lavrov said in Moscow. “There is no other solution.”

Secretary of State John F. Kerry, in Brussels for a meeting of NATO foreign ministers, said he expects to meet with Lavrov later this week for further talks on a proposal for the rebels’ departure that was first discussed Friday.

But hopes of agreement on the new plan to stop the carnage in Aleppo again appeared to falter amid charges, countercharges and confusion. Russian-backed Syrian forces­ made further gains Tuesday in reclaiming rebel-held eastern neighborhoods of the city amid heavy civilian casualties.

Lavrov charged, and U.S. officials sharply denied, that Washington had “revoked” the Friday evacuation proposal. “Serious conversations with our partners do not work,” Lavrov said. He asserted that the United States had notified Moscow that it would not attend a new meeting on the plan.

Lavrov said a U.S.-backed U.N. Security Council draft resolution, which called for a seven-day Aleppo truce with the rebels in place, was proof that other U.S. officials had “disavowed” Kerry’s efforts.

Russia and China vetoed the resolution Monday. They did so, British Ambassador Matthew Rycroft said, “because of their long-standing, misplaced faith in a despot who has killed nearly half a million of his own people.”

Meanwhile, Kerry told reporters here that he was “not aware of any specific refusal” to meet with Lavrov. During a stop Monday in Berlin, he said the two would meet Thursday in Hamburg, where they will attend a meeting of the Organization for Security and Cooperation in Europe.

U.S. officials suggested that Lavrov was trying to avoid ending the conflict while Russia and Syria destroy as much of Syrian President Bashar al-Assad’s opposition as possible. A brutal government offensive over the past week has driven the opposition out of much of the territory in eastern Aleppo it has held since 2012, and the city is thought to be just days from falling.

The U.S. goal, the officials said, is to save as many lives as possible before that happens. They said it was clear from the start of the most recent Kerry-Lavrov talks that the rebels would have to be consulted on a departure plan.

Kerry acknowledged that the discussions with the opposition were ongoing. “We’re not the fighters on the ground; they are,” he said in a news conference. “They have to make their ­choices.” The latest discussions have been about “trying to move people out in order to save Aleppo,” he said. “But until this moment, there has not been agreement on how that would happen.”

International talks began more than two years ago on successive plans to get the opposition and Assad to negotiate a transition government in Syria. That remains the goal, but even as Syria was being destroyed and hundreds of thousands of civilians killed, “the participants were unwilling,” Kerry said. “Both sides.”

He said he hoped that in talks with the Russians this week, “we can get them to understand the importance of getting to that table . . . and not inflaming the situation more . . . with the fall of Aleppo.”

The current evacuation proposal is different from previous plans. Under it, U.S.-backed rebels and civilians would depart the city under secure conditions, leaving only the forces of the al-Qaeda-linked group formerly known as Jabhat al-Nusra.

Russia maintains that the group — which Moscow and Washington deem a terrorist organization — is the only target of the assault on Aleppo. An earlier U.N. proposal called for the group’s fighters to leave the city, with guaranteed secure travel to their stronghold in the neighboring province of Idlib. That would have allowed about a quarter-million civilians under siege in eastern Aleppo, along with opposition forces, to remain and would have facilitated the negotiation of a truce and the flow of humanitarian aid.

Now, the proposal is to evacuate all the civilians who want to leave, along with an estimated several thousand rebels. The evacuation would not include Jabhat al-Nusra, which recently renamed itself Jabhat Fatah al-Sham.

The United States believes that only a few hundred of the group’s fighters are in Aleppo, while Russia insists there are thousands.

But Col. Abu Bakr of Jaish al-Mujahideen, a brigade of the opposition Free Syrian Army, said the rebels have so far rejected the evacuation proposal because they want to “fight to the last drop of blood.” Instead, he said, they are formulating their own plan for evacuating civilians only and transporting them to the rebel-held Aleppo countryside.

“With the civilians gone,” he said, “we will do our best to save what is left of besieged Aleppo.”

Louisa Loveluck in Beirut contributed to this report.