Censor.NET reports citing AFP.
Top diplomats from the four countries, whose leaders hammered out the initial peace plan in the Belarussian capital Minsk, were to meet in Paris, with Kiev accusing Moscow and pro-Russian rebels on the ground of torpedoing the truce.
"The Minsk agreements are not being respected and everyone has to say clearly that this can not go on," a high-ranking Ukrainian diplomatic source told AFP.
Fighting has dropped off significantly since rebels ignored a truce to seize the strategic transport hub of Debaltseve last week, but clashes still continue around strategic flashpoints.
Ukraine's military said its forces in the conflict zone came under fire 12 times overnight and rebels had again tried to storm a village east of key port town Mariupol.
The continuing clashes have delayed a pull-back of heavy weapons that was due to start a week ago under the peace plan. Kiev refuses to withdraw its big guns from the frontline until the shooting stops definitively.
The rebels have claimed several times that they have started to withdraw arms but this has not been confirmed by monitors from the Organization for Security and Cooperation in Europe (OSCE).
The latest fighting came as Putin -- whom Kiev and the West accused of masterminding the conflict -- said he thought the prospect of all-out war between Russia and Ukraine was unlikely.
Asked in an interview with Russian state television if he thought the current situation could lead to a direct confrontation, Putin said: "I think that such an apocalyptic scenario is unlikely and I hope that it will never happen."
"If the Minsk accords are complied with, then I am sure that the situation will gradually get back to normal."
He added: "No one needs a conflict, moreover an armed one, on the periphery of Europe."
Ukraine has accused Russia of sending in more tanks to bolster rebel forces around Mariupol, the latest allegation that Moscow is spearheading the insurgency.
US warns of 'consequences'
Moscow denies it is sending arms and troops to bolster the rebels. However it made similar denials over Crimea -- the Ukrainian Black Sea peninsula that it annexed last year -- before finally admitting that it had deployed troops.
If Mariupol were to fall to the pro-Russian rebels, it would remove a key obstacle to creating a separatist land corridor stretching from Russia's border with Ukraine to Crimea.
Kiev has pressed for UN or EU peacekeepers to be deployed to enforce the peace plan, but that demand has been opposed by Moscow and failed to gain much traction with the West.
"We view this operation as an indispensable instrument to ultimately help implement these agreements and bring peace back," Ukrainian Foreign Minister Pavlo Klimkin told the UN in New York on Monday.
Germany and France brokered the Minsk truce this month in a last-ditch effort to end fighting that has claimed at least 5,690 lives since April, and the peace deal was subsequently endorsed by the UN Security Council.
Up to now, the main act of compliance with the Minsk agreement has been a prisoner swap conducted on Saturday in which nearly 200 captured fighters from both sides were traded.
The United States and the European Union have strongly warned against further breaches of the ceasefire, with Washington saying extra "consequences" could be imposed on Russia within days.
Russia has already been hit by successive rounds of Western sanctions, savaging its economy, which is headed for recession because of a collapse in oil prices.
Meanwhile, Russia's state-owned gas giant Gazprom warned Tuesday it could cut off gas deliveries to Ukraine within two days, upping the stakes in the crisis there -- and threatening supplies to the rest of Europe.
Max Delany, AFP
The Russian President Vladimir Putin ruled out an 'apocalyptic scenario' of a full-scale war in Ukraine, amid continuing shelling of Ukrainian territories and troops by the Russia-backed terrorists despite the agreed cease-fire.
Censor.NET reports citing AFP.