Early reports from eastern Ukraine say the country's "Day of Silence" truce between government troops and pro-Russian separatists is being largely observed.
President Petro Poroshenko, who announced last week that Ukraine's military would halt fire on December 9, said that thus far the cease-fire was holding.
He said in a lecture in Singapore that "we don't have one shot [fired], we don't have any soldiers killed."
The truce coincided with the resumption of supplies of Russian gas to Ukraine after a six-month suspension that began when Moscow turned offf the taps as tension mounted between the two former Soviet republics.
Poroshenko, in remarks to a group of business executives, academics, and diplomats in Singapore, said that Ukraine was ready to "stop the bleeding" but not at the expense of "giving up" its freedom, democracy, sovereignty, and independence.
Reports from the cities of Luhansk and Donetsk, two separatist-held provoncial capitals in eastern Ukraine, said early on December 9 that the truce was largely being observed.
Aleksandr Zakharchenko, a rebel leader in the self-proclaimed Donetsk People's Republic, said the situation in Donetsk "is now quiet" after early morning shelling.
Ukrainian Defense Ministry spokesman Valentyn Buryachenko said only that one mortar strike in Luhansk had been registered, Interfax reported.
The conflict has killed more than 4,300 people and forced hundreds of thousands to flee their homes.
Pro-Russian separatist leaders had voiced support for the truce plan, and intense shelling took place until right before the start of the cease-fire.
Ukrainian military officials said on December 8 that in the 24-hour period before the truce began, residential areas and government forces had been hit by rocket fire more than 60 times.
They said two civilians were killed and 10 others wounded by the artillery attacks.
Separatist officials in Donetsk said two civilians were killed in that rebel-controlled city and some 20 buildings damaged by mortar fire.
Meanwhile, Poroshenko is trying to organize a new round of peace talks in Minsk that would involve Ukrainian, Russian, and separatist representatives along with the Organization for Security and Cooperation in Europe.
Ukraine had pushed for the talks to be held on December 9, but the separatists wanted them held later.
Vasiliy Vovk, the head of Ukraine's security services' investigative department, said late on December 8 that on television that the Minsk peace talks would take place on December 12.
The rebels accused Kyiv of "bad faith" in reaching a long-term peace agreement after it cut off pension payments and other basic social services to the eastern areas controlled by rebels.
Ukraine made that move after the separatists held November 2 elections denounced by Kyiv and the West as illegal and in violation of a September 5 deal on a cease-fire and steps toward peace.
The United States, the European Union, and other Western nations have placed economic sanctions on Russia for its annexation of Crimea from Ukraine in March and its support for the pro-Russian separatists who control parts of the Donetsk and Luhansk provinces.
Moscow denies it has sent troops or weapons into Ukraine despite what Kyiv and NATO say is clear evidence of a direct military role.
The Ukraine crisis began in November 2013, when then-President Viktor Yanukovych abandoned plans for an agreement on closer trade relations with the European Union in favor of closer ties with Moscow.
The move sparked huge protests that toppling Yanukovych in February.