(CNN) -- The leaders of Ukraine and Russia talked peace on Thursday amid the longstanding tensions between the countries over the grinding unrest in eastern Ukraine.
Ukrainian President Petro Poroshenko and Russian President Vladimir Putin chatted over the telephone, according to Poroshenko's office. Putin also spoke with the German and French leaders amid regional concern over the crisis.
Poroshenko discussed the main points and the implementation of a peace plan for eastern Ukraine, where Ukrainian authorities have been at odds with pro-Russia separatists.
Putin, according to the statement, backs an effort to de-escalate tensions in eastern regions and a process to forge a cease-fire and a peace plan.
Russia and Ukraine have been engaged in a tense standoff since March, when Russia annexed Crimea and massed troops along its border with Ukraine.
In recent months, there have been pro-Russian separatist stirrings in the eastern regions of Donetsk and Luhansk.
Ukraine's government in Kiev has accused Russia of allowing weapons and military equipment, including tanks, to cross the border illegally into the hands of pro-Russia separatists.
On Wednesday, Poroshenko announced plans to implement a unilateral cease-fire to ease the crisis in the restive eastern part of the country.
Ukrainian forces are putting their arms down only briefly, he said, referring to a time in which he expects separatist groups to disarm.
The plan 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.
The plan would also include the closure of the Ukraine-Russia border and changes to the constitution to decentralize power.
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.
Putin spoke about Ukraine in a phone conversation with German Chancellor Angela Merkel and French President Francois Hollande.
They called for "an early halt to the fighting in eastern Ukraine, in order to stabilize the security situation and to create the conditions for a real de-escalation," Hollande's office said.
Citing Poroshenko's unilateral peace effort, the two leaders asked Putin "to make every effort to convince armed groups and move as quickly as possible towards a cessation of hostilities. Otherwise, the international community may adopt further measures that would affect relations with Russia."
Amid international talks, the fighting continues. Ukraine's government has been carrying out what it calls an anti-terrorist operation, centered in the Donetsk and Luhansk regions, to try to regain control from pro-Russian separatists.
At least four Ukrainian troops died in clashes with militants Thursday, military spokesman Vladislav Seleznyov said. He said 200 militants were killed in fighting.
NATO spots Russian military buildup
NATO, meanwhile, has seen a "new Russian military buildup" near the border with Ukraine, NATO chief Anders Fogh Rasmussen said Thursday, a development that may alarm Kiev and the West.
Rasmussen, responding to a question from a Russian journalist at an event in London, warned that any Russian intervention across the border could prompt tougher international sanctions.
"Yes, I can confirm that we now see a new Russian military buildup -- at least a few thousand more Russian troops deployed to the Ukrainian border, and we see troop maneuvers in the neighborhood of Ukraine," Rasmussen said.
Of the new forces, Rasmussen said, "If they're deployed to seal the border and stop the flow of weapons and fighters, that would be a positive step. But that's not what we're seeing. I consider this a very regrettable step backwards and it seems that Russia keeps the option to intervene further."
Rasmussen warned that "the international community would have to respond firmly if Russia were to intervene further. That would imply deeper sanctions which would have a negative impact on Russia."
The United States and European Union already have imposed economic sanctions on targeted individuals and firms in Russia.
In his speech at Chatham House, a London-based think tank, Rasmussen talked of plans for a future NATO that, he said, "answers the questions raised by the new security realities of the 21st century."
Rasmussen is also due to meet Thursday with UK Prime Minister David Cameron and Foreign Secretary William Hague.
Ukraine will sign an Association Agreement with the European Union on June 27, Poroshenko's office said late Wednesday.
Such treaties create a framework for across-the-board cooperation with the EU, and in certain cases are viewed as a step toward membership in the EU.
Displeasure with the pro-Russian stance of Ukraine's former president was among the reasons for the protests that led to his leaving office. Poroshenko, who is pro-EU, is moving Ukraine to closer partnerships in Europe.