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"I take the point of view that Russia would not have proposed anything if they weren't prepared to get into a negotiation about it," said Volker in an interview Monday with VOA's Ukrainian Service chief Myroslava Gongadze.

"They haven't done anything for three years on this. They haven't proposed a peacekeeping force before. As recently as a couple weeks ago, they were saying that they would never want the U.N. there. So, the fact that they opened this conversation, to me, is an indication that they are willing to discuss it."

Russia's proposal earlier this month at the U.N. called for peacekeepers along the line of conflict in eastern Ukraine, but not along the Russia-Ukraine border where weapons and fighters can easily cross.

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Volker called it a "very narrow concept" that would have the effect of dividing the country even further.

Read alsoVolker: Russia's aggression in Ukraine fails to achieve its goals, has opposite effect"That's not acceptable to anybody and does not restore the territory," he said. "On the other hand, if we can establish a peacekeeping force and build that concept into one that is covering the entire contested area, that is containing heavy weapons and that is controlling the Ukraine-Russian border from the Ukrainian side, then there is a lot of promise in that."

"That's where both governments are right now seeing whether it is possible to expand this concept into one that would be truly meaningful and helpful," he added.

Russia's growing costs

Russia's costs for maintaining the conflict in Ukraine have only gone up while benefits the Kremlin may have expected have not panned out, said Volker. Russia has lost influence in Ukraine while Western support for Kyiv has increased along with sanctions against Moscow.

"So, for all of these reasons, the costs are increasing. Even the financial costs of just maintaining the Donbas, and they're not getting anything out of it. So, that at least opens the door to thinking maybe Russia would like to try something else," Volker said.

"Ultimately, I think it really boils down to Russia's decision-making," he added. "Do they want to resolve the crisis in Ukraine, get their forces out, and re-establish Ukraine's territorial integrity or, do they not want to do that? If they want to dig in and create another Abkhazia [breakaway region of Georgia supported by Russia], they can do it. But, that's a very costly proposition for Russia."

Read alsoKremlin furious over draft UN Resolution calling Russia "aggressor state"A 2015 peace deal Russia signed with Ukraine, Germany, and France in Minsk has failed to come to fruition as Kyiv and Moscow blame each other for not moving on the plan.

"The problem with the Minsk agreement is that it was becoming a circular argument that was going nowhere," said Volker. "The Russians are saying ‘no, Ukraine has to do the political steps.' Ukraine says, ‘it can't do the political steps because it can't even access the territory.' And, then how can we go to the Rada [Ukrainian parliament] and get a vote when nothing has happened on a ceasefire in three years. So, it's stuck that way and I think, in some respects, some of the actors found that to be conveniently stuck."

Volker said the U.S. role was to try to unstick the Minsk deal.

"If we can get to a more strategic level of decision-making with Russia and, frankly, with our European partners and with Ukraine, then if we can create political will, Minsk is a perfectly fine vehicle for implementation," he said.

In August, the U.S. envoy met with Kremlin aide Vladislav Surkov in Minsk. Surkov is considered the architect of Russia's strategy on Ukraine and its military backing for separatists in eastern Ukraine's Donbas region.

Status quo: Bad for all

"When we met in August, one of the things we agreed is that the status quo is not good for anybody," said Volker. "It's not good for Russia, it's not good for Ukraine, it's not good for the people of the Donbas. So we should be exploring to see if there is something else that would be better."

More than 10,000 people have been killed in eastern Ukraine since fighting between government forces and Russia-backed separatists broke out in early 2014.

Volker said the U.S. is still considering supplying lethal, defensive weapons to Ukraine's military forces.

"I don't have anything new to say on timing of this sort of thing [possibly selling lethal, defensive weapons to Ukraine]," he said. "But, I can say that it's taken very seriously in the administration and there are people working very hard at it."

Volker said the U.S. would seek progress in eastern Ukraine separate from the issue of Crimea, the Black Sea peninsula that Russia annexed from Ukraine in March 2014.

"If we are able to make progress in one area the Donbas let's do it. Let's make progress, let's see if we can get that territory back," he said. "At the same that doesn't change at all our refusal to accept the annexation of Crimea and grant any legitimacy to Russia's actions."

Budapest memorandum

The U.S. envoy acknowledged more should have been done to back up the 1994 Budapest Memorandum, which was signed when he was a mid-level diplomat at the U.S. Embassy in Budapest and should have prevented Russia taking Crimea.

"The only country violating the Budapest Memorandum is Russia. So, France didn't invade Ukraine. U.K. didn't invade Ukraine. Only Russia invaded Ukraine," Volker said.

Read alsoBudapest Memorandum provides less security than one nuclear charge – PoroshenkoUkraine agreed to give up its Soviet-era nuclear weapons in return for guarantees of territorial integrity and sovereignty under the deal signed by Russia, the U.K., and U.S. But, when Russian forces began taking over Ukraine's Crimea military bases, none of those who signed the memorandum attempted to stop them.

"We should have done more immediately," said Volker. "It's important for Ukraine itself. It's important for the principle that it establishes about non-proliferation of nuclear weapons. And, so, unfortunately, when Russia invaded, we didn't do enough on that."

The U.S. envoy said all that can been done now is go forward to help restore Ukraine's territorial integrity. "If we do that, we'll be taking a step towards the fulfillment of Budapest," he said.

Peacekeeping Forces

Volker, who President Donald Trump made special envoy in July, shot down suggestions that Russians could be among any peacekeepers deployed to Ukraine.

"I think the U.N. standards themselves are that neighboring countries should not be involved in peacekeeping in neighboring states," he said. "And, certainly in this case since Russia has been a party to the conflict it would clearly not make sense."