The Ukrainian army and pro-Russian rebel forces are laying down their arms in an attempt to revive a September cease-fire.
The sides have promised to suspend hostilities as part of Tuesday's so-called "Day of Silence."
The cease-fire appeared to be mostly holding, although scattered clashes were reported.
Peace talks also had tentatively been planned, but Kyiv officials said negotiations will probably not begin until Friday, at the insistence of the rebels.
Fighting has continued in eastern Ukraine since the signing of the September 5 cease-fire agreement, claiming nearly 1,000 lives, and the two sides have accused each other of violating the truce.
Kyiv accuses Russia of providing arms and other support to the separatist forces, a charge Moscow denies.
Meanwhile, German Chancellor Angela Merkel has again strongly criticized Russia's actions in Ukraine.
She told a convention of her Christian Democratic Party on Tuesday that "what’s been happening for months in Ukraine threatens Europe’s peaceful order," accusing Russia of violating international law and trying to create "spheres of influence."
Still, the German leader said she was convinced the Ukraine crisis could be resolved diplomatically.
In an interview published in the Sunday edition of Germany's Die Welt newspaper, Merkel accused Russia of breaking a 1994 agreement guaranteeing Ukraine's sovereignty and territorial integrity, and of having created difficulties for Ukraine, Georgia and Moldova after they made sovereign decisions to sign agreements with the European Union.
For his part, Russian Foreign Minister Sergei Lavrov said Tuesday that Germany "has traditionally played a very constructive role" in the EU's ties with Russia, but that if it switched to a policy of "diktat" - or issuing orders - neither Europe nor Germany would benefit.
Meanwhile, Ukraine has begun receiving its first cross-border natural gas shipments since Moscow cut off supplies in June in a bitter pricing dispute.
Analysts say the renewed gas flow, which comes after lengthy negotiations over pricing and arrears, may provide Ukraine with enough energy to heat homes through the worst months of the Eurasian winter.