Russian President Vladimir Putin has backed Ukraine's ceasefire plan and appealed to both sides to halt all military operations.
A Kremlin statement issued today said: "The president of Russia calls on the opposing sides to halt any military activities and sit down at the negotiating table."
The statement said Mr Putin supported Ukrainian President Petro Poroshenko's decision to order Ukrainian troops to observe a unilateral ceasefire starting last night.
Mr Poroshenko said the week-long ceasefire is the first step in a peace plan which would include an amnesty for pro-Russian separatist fighters.
Mr Putin however said that without action directed at starting talks, the plan was "not viable and unrealistic"
Earlier, pro-Russian separatists in Ukraine's embattled east dismissed the ceasefire as fake, while nine Ukrainian service members were wounded in clashes within the first few hours.
Separatist leader Pavel Gubarev said in Donetsk that "there is shooting all the time, and this ceasefire that Poroshenko is talking about is just fake".
Otherwise, however, no large-scale fighting was reported on the opening day.
Mr Poroshenko ordered the ceasefire starting at 10pm yesterday as a first step in a peace plan that is to include an amnesty for fighters who lay down their arms, and a chance for them to leave the country.
That is to be followed by local and parliamentary elections and a jobs programme.
Separatist leaders have rejected the ceasefire and said they will not disarm.
In Donetsk, a group of armed men gathered in the central square to take a military oath to the self-proclaimed Donetsk People's Republic.
Mr Gubarev, who describes himself as the governor of the Donetsk People's Republic, said there was no ceasefire near Slovyansk, scene of serious clashes over the past several months.
"There is no ceasefire over there," Mr Gubarev said. "There is shooting all the time, and this ceasefire that Poroshenko is talking about is just fake. The Ukrainian forces are either not under his control, or he is just a liar."
The Ukrainian Border Guard Service reported overnight attacks on two border posts in the Donetsk region, which left three troops injured, hours after the ceasefire was announced. One of the posts, Vyselky, was attacked with mortar and sniper fire for half an hour, the border guards said.
An attack on another border post, Izvaryne, immediately before the ceasefire left six men injured, the Border Guard Service said.
Ukraine's Defence Ministry reported two attacks on the quarters of a missile unit in the village of Avdiyivka. Kiev said men armed with automatic rifles and grenade launchers attacked the base at 11pm - one hour after the ceasefire was announced - prompting the army to respond. The rebels left in the morning, the defence ministry said.
The UN says 356 people have died in violence in Ukraine since May 7, and 34,000 have left their homes.