Russia circulated a draft resolution in the U.N. Security Council Monday to end the violence in eastern Ukraine while skeptical members of the Western Council urged Moscow to consider its next move, even as clashes continued between Ukraine's government forces and pro-Moscow separatists in the region.

The 15-member council was reportedly briefed by Russian officials behind closed doors, where they called for a permanent solution to restore peace in the eastern part of the country and presented a draft proposal, which was questioned by Western nations who accuse Russia of fuelling discontent and violence that has raged on for weeks in the region. 

"There was some positive reactions from some members of the council. However, others were asking so many questions that if we were to try to answer them then we would be talking about things for weeks," Russian U.N. Ambassador Vitaly Churkin, said, after the meeting, according to Reuters, adding: "We have not yet decided what out next move is going to be in terms of working on this resolution."

While Ukraine's newly-elected President Petro Poroshenko has launched military operations in the region to control the violence, on Tuesday, Arsen Avakov, Ukraine’s Minister of Internal Affairs, warned the local population, on his Facebook page, to stay indoors to avoid risking their lives after a blast in the Luhansk region killed at least seven people Monday. The post also mentioned that another military operation was taking place in Slovyansk, where heavy gunfire could be heard, and engineering facilities had reportedly been destroyed.

“If they are going to call for or would support a reduction in tensions and a de-escalation, it would be more effective for them to end those activities," U.S. State Department spokeswoman Jen Psaki said, referring to Russia's actions in the region, according to Reuters.

Russia has also threatened to cut off the supply of natural gas to Ukraine after the latter said Friday that it would pay $786 million of the estimated $5.2 billion it owes Russia through the end of May.

U.S. President Barack Obama is reportedly scheduled to visit Europe this week and is expected to meet Poroshenko and possibly even Russian President Vladimir Putin during the World War II anniversary ceremonies in France.

While the U.S. and Kiev blame Russia for supporting rebel fighters who have demanded to secede from Ukraine, Russian officials have responded by stating that Western countries' belief that the situation in the region would improve after the May 25 elections, has backfired.

“Everything is happening in exactly the opposite way,” Sergei Lavrov, Russia’s foreign Minister said, according to Reuters on Monday, adding: “People are dying every day. Peaceful civilians are suffering more and more - the army, military aviation and heavy weapons continue to be used against them.”