A statement released by the French presidency has reportedly asserted that France and Germany believe that the Minsk ceasefire agreement is "generally" holding in east Ukraine.
However the leaders of the two nations pointed out that some "local incidents" must be "quickly" resolved, reported the BBC.
Although fighting is reported to have died down after the new truce deal took effect, yet shelling continued around the besieged town of Debaltseve.
OSCE monitors agreed that the truce seemed to be "generally holding," but added that they had been denied access to Debaltseve.
Meanwhile, a military spokesman said that Ukrainian troops faced shelling at least 60 times in the hours after the truce came into force.
He added that Debaltseve, a key transport hub, had been the site of most clashes.
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The statement released by the French presidency also said that the four nations, France, Germany, Ukraine and Russia, who negotiated the ceasefire agreement last week, held more talks on Sunday and agreed to implement the next stage of the new Minsk deal.
The nations agreed that stopping the fighting was just the first step and should be followed on day two of the ceasefire by the start of the withdrawal of heavy weapons to create two demilitarised 50-140 km wide buffer zones.