As reported by Censor.NET citing Radio Free Europe/Radio Liberty, Volker's comments to reporters on Jan. 29 came three days after his meeting with his Russian counterpart, Vladislav Surkov, in the Persian Gulf city of Dubai.
Prior to those talks, Volker had traveled to Kyiv for meetings with Ukrainian President Petro Poroshenko and other government officials and political leaders.
Volker said he conveyed to Surkov in a phone call earlier this year "a very strong sense of disappointment and frustration in Washington that Russia has done absolutely nothing to end the conflict [in eastern Ukraine], or to withdraw its forces."
After that, Volker said, he and Surkov "had a very detailed discussion" about how the two sides could break the impasse, including U.S. hopes for peacekeepers with a broad mandate to patrol the entire conflict zone -- including the Ukrainian-Russian border.
Only then, Volker told reporters on January 29, would it be possible "to create the conditions for implementing the Minsk agreements" -- September 2014 and February 2015 pacts aimed at resolving the conflict.
"There was more openness...to talking about how we'd get there," Volker said of the Russian side's approach during the Dubai talks.
Surkov was quoted by Russia's state-run TASS news agency as saying that U.S. suggestions on deploying a UN peacekeeping mission looked "doable" and that Moscow would study them carefully.
The tone following the Dubai meeting was notably more optimistic than after the envoys' November talks in Belgrade, which Volker called "a step back."
Discussions about deploying a UN peacekeeping force ramped up in September, when Russian President Vladimir Putin proposed deploying a UN-led mission along the line separating Ukrainian government forces and the Russia-backed forces.
But common ground on the issue has proved elusive.
Kyiv and the West worry that the deployment of peacekeepers only along the front line rather than the Russian-Ukrainian border would cement Russian control over separatist-held territory and allow Moscow to continue sending fighters and weapons into Ukraine.
Volker said he and Surkov also discussed other issues the U.S. hopes can be addressed immediately, including the return of Russian officers to the Joint Center for Control and Coordination (JCCC) to facilitate communications and improve the cease-fire.
Russia pulled its officers from the JCCC in December, accusing the Ukrainian side of obstructing their work and limiting access to the front line.
Volker said they also discussed the possibility of increasing the number of crossing points for civilians in the conflict zone, and the restoration of mobile-phone service, which had been cut recently.
The two also talked about possible future prisoner exchanges following a large swap that took place in December, as well as increased access for international humanitarian groups, Volker said.
On Sept. 5, Russian President Putin said deployment of U.N. peacekeepers in the Donbas was quite appropriate for solving of the conflict in the region, but only along the line of contact and with the aim of protecting the OSCE mission.
Ukraine's representative in Humanitarian subgroup of the Tripartite contact group in Minsk talks, deputy speaker of Ukrainian parliament Iryna Herashchenko commented on Putin's statement and said the Kremlin scenarios will fail; peacekeepers must be introduced across all Russia-occupied territories.