Kiev (CNN) -- Ukrainian President Petro Poroshenko declared the start Friday of his anticipated cease-fire in the fight against separatists in the country's pro-Russian east.
He said military units will respond only if they're attacked, and warned militant fighters to abandon their weapons before the cease-fire expires on June 27.
"Those who will not lay down their weapons will be destroyed," Poroshenko said, according to a statement issued by the Interior Ministry.
Despite Poroshenko's declaration, the Russian Foreign Ministry said one of its border units in Novoshahtinsk was shelled Friday, injuring one customs officer.
"It is a direct provocation, which aims to prevent the implementation of the Geneva Agreement and immediate de-escalation of Ukrainian domestic conflict," the ministry said.
Ukraine denied it fired artillery or mortar at the Russian unit.
The Ukrainian Defense Ministry said in a statement that during the anti-terrorist operation, its forces approached Dolzhansky and militants, who recently occupied this border unit, responded with fire towards Ukrainian forces. A mortar mine exploded near the border line, according to the Ministry.
Poroshenko had announced Wednesday plans for the cease-fire.
He and Russian President Vladimir Putin spoke by phone Thursday, according to Poroshenko's office.
It was not immediately clear what impact the cease-fire was having.
Putin, according to the statement, backs an effort to de-escalate tensions in eastern regions and a process to forge a ceasefire and a peace plan.
Still, NATO chief Anders Fogh Rasmussen said Thursday that the military alliance had seen a "new Russian military buildup" near the border with Ukraine.
This, Rasmussen said, involved "at least a few thousand more Russian troops deployed to the Ukrainian border, and we see troop maneuvers in the neighborhood of Ukraine."
The U.S. government also believes that additional Russian tanks have been deployed as potential reinforcements for separatists in Ukraine, a senior administration official said Friday.
President: Free hostages
Poroshenko's cease-fire includes the closure of the Ukraine-Russia border and changes to the constitution to decentralize power.
It also offers amnesty to those who didn't commit serious crimes, the President said. An escape corridor will be offered for those who disarm to leave Ukraine.
"We expect that hostages and seized premises will be liberated. We expect that a large number of civilians will use the security guarantees for the citizens of Donbas," Poroshenko said, referring to Ukraine's eastern region.
In his conversation with Putin, Poroshenko stressed the need for the release of Ukrainian hostages and to establish effective security controls on the border with Russia.
Poroshenko also met Thursday with representatives of the "legitimate authorities" in Donetsk and Luhansk regions, his office said. They discussed ways to decentralize power and revive the region's economy.
Calls to reduce tensions
Russia and Ukraine have been engaged in a tense standoff since March, when Russia annexed Crimea and massed troops along its border with Ukraine.
Before the cease-fire took effect, the speaker of Ukraine's parliament told lawmakers on Friday that Ukrainian forces had completed an operation to close off the country's eastern border with Russia.
Troops and separatist fights clashed in Artemovsk and Luhansk on Thursday night before the ceasefire went into effect, a government spokesman said.
Ukraine's government in Kiev has accused Russia of allowing weapons and military equipment to cross the border illegally into the hands of pro-Russia separatists, who have led uprisings in Ukraine's eastern Donetsk and Luhansk regions.
The United States is calling on the Russian government to cease its activities in eastern Ukraine as Poroshenko implements his cease-fire plan, a senior administration official said Friday.
The official warned the Russian government of potential for more sanctions if these activities continue. The Treasury Department on Friday released new sanctions for seven Ukrainians who are separatist leaders.
Journalist Victoria Butenko reported from Kiev and CNN's Laura Smith-Spark wrote in London.