Western fears of wider confrontation have continued to spiral after NATO said Russia had sent troops to fight in Ukraine.
NATO has told Russia to halt its "illegal" military actions in Ukraine after the West accused Moscow of direct involvement in the escalating conflict.
Western fears of wider confrontation have spiralled after NATO said Russia had sent troops to fight in Ukraine and funnelled huge amounts of heavy weaponry to the pro-Kremlin rebels.
"We condemn in the strongest terms Russia's continued disregard of its international obligations," NATO chief Anders Fogh Rasmussen said on Friday after an emergency meeting of the alliance on the crisis.
"We urge Russia to cease its illegal military actions, stop its support to armed separatists, and take immediate and verifiable steps towards de-escalation of this grave crisis."
Kiev and the West have accused Russian troops of being behind a lightning counter-offensive that has seen the rebels seize swathes of territory from Ukrainian government forces, dramatically turning the tide in the four-month conflict.
And in a move certain to anger Kiev's former masters in Moscow, Rasmussen also said NATO was not closing the door to Ukraine's possible membership of the transatlantic alliance after the government said it wanted to join.
Russian President Vladimir Putin has repeatedly denied Moscow is fuelling the conflict or having any troops on the ground in the former Soviet state.
And on Friday, he demanded that the Ukrainian government hold "substantial" talks with the separatists who took up arms against Kiev in April, apparently emboldened by Russia's annexation of Crimea the month before.
"I believe that what is happening in Ukraine right now is in principle our common colossal tragedy and it is necessary to do everything for it to stop as soon as possible," he said.
The new rebel advance has raised fears that the Kremlin could be seeking to create a land corridor between Russia and Crimea, the strategic Black Sea peninsula.
The sharp escalation came just days after Putin held talks with Ukraine's President Petro Porokshenko but failed to make any significant breakthrough.
NATO on Thursday said Russia had sent at least 1,000 troops to fight alongside the rebels, along with air defence systems, artillery, tanks and armoured vehicles, and had massed 20,000 troops near the border.
"Russia has deliberately and repeatedly violated the sovereignty and territorial integrity of Ukraine, and the new images of Russian forces inside Ukraine make that plain for the world to see," US President Barack Obama said.
"This ongoing Russian incursion into Ukraine will only bring more costs and consequences for Russia."
Concerns that Kiev could be drawn closer into the Western security alliance - and towards Europe - are seen as a key motivation behind Russia's actions in recent months.
But Putin dismissed the Western pressure, symbolically describing the insurgents as the defenders of New Russia, a Tsarist-era term for Moscow's former imperial holdings in the region that the strongman has revived since annexing Crimea.
He praised rebel successes in halting Kiev's advances in a counter-offensive in the southeast that has left government troops battling for survival in the town of Ilovaysk.
He called on rebel forces to open a "humanitarian corridor" for the besieged Ukrainian troops.
Top rebel leader Alexander Zakharchenko - who has said the Russian troops in Ukraine were "on holiday" - told Russian television that his men would be willing to let government troops withdraw if they give up their weapons.
Ukrainian security chiefs lashed out at the Russian proposal, saying in a statement it proved rebels were "controlled directly from the Kremlin".
According to new UN figures, almost 2600 people have been killed since mid-April, and well over 400,000 have fled their homes.
The latest tensions sent the Russian ruble nosediving to a record low against the dollar on Friday and pushed stock markets down.
German Chancellor Angela Merkel has said European leaders would discuss possible new measures against Moscow at a summit in Brussels on Saturday.
The United States and the European Union have already imposed a series of punishing sanctions on Moscow over the crisis, the worst standoff between Russia and the West since the Cold War.
At an emergency UN Security Council meeting on Thursday, US envoy Samantha Power demanded that Russia "stop lying".
"We see Russia's actions for what they are: a deliberate effort to support and now fight alongside illegal separatists in another sovereign country."
Kiev said Thursday that Russian soldiers had seized control of a key southeastern border town and a string of villages, with fears that the rebels could threaten the government-held port town of Mariupol.