Ukraine's president has ordered his forces to cease fire and halt military operations for a week against pro-Russian separatists in the country's east.
It is the first step in a peace plan he hopes will end the fighting that has killed hundreds.
The Kremlin dismissed the plan, saying it sounded like an ultimatum and lacked any firm offer to open talks with insurgents.
Petro Poroshenko, making his first trip to the east as Ukraine's president, said that the ceasefire will run until the morning of June 27 and that his troops reserve the right to fire back if separatists attack them or civilians.
"The Ukrainian army is ceasing fire," he said in a statement. "But this does not mean that we will not resist. In case of aggression toward our troops, we will do everything to defend the territory of our state."
Separatists in the Donetsk and Luhansk regions have declared independence from his government in Kiev, occupied public buildings and fought with heavy weapons against Ukrainian troops.
Rebel leaders have already dismissed Mr Poroshenko's plan, and it remains to be seen whether they will comply and how much pressure Russia will put on them to cease fire.
The Kremlin denies supporting the insurrection and has said that Russians fighting in Ukraine are doing so as private citizens.
Russia said in a statement that an initial analysis of Mr Poroshenko's plan shows that "it's not an invitation for peace and talks, but an ultimatum" to insurgents in south-east Ukraine to lay down their weapons. It said the plan "lacks the main element - an offer to start talks".
The Kremlin said Mr Poroshenko's government issued the peace plan "deliberately or accidentally" at roughly the same moment that Ukrainian forces fired into Russian territory, wounding a Russian customs officer. It said the Russian side was waiting for Ukrainian "explanations and excuses" over the attack.
The Ukrainian defence ministry said that its forces were trying to flush out insurgents near the border checkpoint, but denied targeting it.
Leonid Slutsky, a senior lawmaker in the lower house of Russian parliament, said President Vladimir Putin could be waiting to see concrete action by the Ukrainian forces to stop fighting.
"That will be a proof that Poroshenko is indeed the president. That could be considered the first step toward peace," Mr Slutsky said.
Mr Putin has criticised Ukraine's military operation against the rebels but he has resisted both the rebels' pleas to join Russia and appeals from Russian nationalists to send troops into Ukraine.
The White House and European leaders urged support for the plan.
White House spokesman Josh Earnest said the US government "has been very clear in our support for President Poroshenko's effort to bring peace and unity to Ukraine". He added the White House wants Russia "to stop supporting the militants who are fomenting so much violence and instability".
Tension between Russia and Ukraine escalated sharply in February when protests in favour of closer ties with the European Union drove president Viktor Yanukovych from power. Russia denounced the events as a coup and annexed Ukraine's mostly Russian-speaking Crimea region. The rebellion in the eastern regions broke out shortly afterwards, with Ukraine accusing Russia of supporting it.
Mr Poroshenko's ceasefire is intended to give separatists time to lay down their arms and to allow fighters from Russia to safely leave the country.
The proposed next steps include joint security patrols to prevent looting and other crime, new local and parliamentary elections, and measures to protect the language rights of Russian speakers in the east.
In the longer term, Mr Poroshenko has suggested decentralising power to give the country's regions more political authority.
At a border crossing near Izvaryne in the separatist Luhansk region, 100 or more cars waited in line for hours to cross from Ukraine into Russia as people fled the unrest. Some cars were piled high with possessions.
One car had a sign on the windshield that said "children". A man named Sergei, who would not give his last name for fear of retaliation, said, "People are simply leaving everything and trying to escape the war."
The United Nations says at least 356 people have been killed since May 7 and 34,000 have fled their homes. The UN report does not include casualties from previous weeks of fighting, so the actual toll could be significantly higher.