Pro-Russian armed men take positions near the
Pro-Russian armed men take positions near theReuters

Moscow and Kiev have reached a "mutual understanding" to end the prolonged fighting in Ukraine's embattled east late Monday, after a round of last-minute talks between Ukrainian President Petro Poroshenko and Russian President Vladimir Putin. 

The Ukrainian Foreign Ministry said in a brief statement in Kiev that Russian and Ukrainian representatives had met three times in the past two days to discuss Poroshenko's plan to end fighting between the Ukrainian military and Russian separatists. 

"As a result of the work, the sides reached a mutual understanding on key stages of the implementation of the plan and on a list of priorities which will contribute to a de-escalation of the situation in the Donetsk and Luhansk regions of Ukraine," it said.

Poroshenko himself made clear, in a series of brief remarks Monday, that he is aiming to end the bloodshed as quickly as possible. 

"We have to stop fire this week," he said. "For me, every day of people dying, every day of Ukraine paying such a high price is an unacceptable one."

Meanwhile, a fierce battle rages in the former city of Slaviansk since Sunday, which reporters at the scene say has become a war zone. The city, which the separatists officially took in April, is quickly running out of resources, locals told CNN; electricity, water, and telecommunications have been utterly cut off - and people are beginning to starve. 

The Ukrainian army has been firing artillery at government compounds, separatist officials in the town told the Russian news agency ITAR-TASS. The separatists stated that artillery fire had been aimed at the former Security Service compound, the city administration building, and Police Department. One local militia official stated that "there were victims among civilians as many were injured by shrapnel."

Despite Moscow's repeated commitment to maintain peace in the region, accusations continue to fly that Putin has directly sent soldiers in to bolster the pro-Russian separatist movement. 

Witnesses reported seeing Russian Kamaz military transport vehicles break through frontier posts into Ukraine, according to Reuters.

And then there are the Cossacks, seasoned Russian fighters who told CNN and Reuters correspondents that they had been helping fighters in and near Slaviansk for over two months. 

At the rebel-held Chervonopartizansk checkpoint into Russia, one Cossack - identified only as Alexander - boasted that his group had caused members of a Ukrainian border police squad to flee from the checkpoint they were manning - taking their wives and families with them. 

"We let them go with their weapons to avoid a fight," he stated, with a grin. "Since their position was weaker, we would have had to kill them." 

Last week, Russian authorities insisted to international media that as many as 4,000 people - mostly women and children - had fled across the border to Western Russia after the Ukrainian military assault, seeking asylum. Ukrainian authorities continue to deny or downplay the claim. 

Putin, in the interim, has ordered border guards to stop the illegal crossings of people from Ukraine by beefing up security, the state-run ITAR-Tass news agency reported Saturday.