DONETSK, Ukraine (AP) -- Pro-Russian insurgents in eastern Ukraine agreed Monday to respect a cease-fire declared by the Ukrainian president, raising hopes for an end to months of fighting that have killed hundreds and ravaged the country's industrial heartland.
The announcement came as the Russian and U.S. presidents traded demands over the conflict. Russian President Vladimir Putin urged direct talks between the government and the rebels. President Barack Obama warned Putin that Moscow will face additional costs if it does not help ease the crisis.
The insurgents' pledge to respect the cease-fire came on the first day of talks between a former Ukrainian president, the Russian ambassador, European officials and the eastern separatists who have declared independence. While the government side was nominally not represented, ex-President Leonid Kuchma attended the discussions at the request of the sitting president.
The negotiations were launched in line with President Petro Poroshenko's peace plan, which started Friday with a weeklong unilateral cease-fire in the fighting that has killed more than 350 people and forced tens of thousands to flee their homes.
Alexander Borodai, one of the rebel leaders who took part in Monday's talks in Donetsk, said rebels would respect Poroshenko's cease-fire, which lasts through 0700 GMT (2 a.m. EDT) Friday.
The insurgents had previously demanded the Ukrainian military withdraw its troops from the east as a condition for any talks, so Borodai's statement represented a softened stance that raised expectations that the cease-fire could hold. Even before the insurgents made their pledge, the government said that there had been no fighting in the east since Monday morning.
Since the cease-fire was declared Friday, the Ukrainian government has accused the rebels of firing at government positions, while insurgents blamed Ukrainian forces for failing to honor the promise to halt hostilities. Poroshenko has said government troops will fire back if attacked.
The rebels, who have declared regions on border with Russia independent and fought government troops for two months, also promised to release observers from the Organization for Security and Cooperation in Europe who have been held hostage.
"This will be one of the steps that will improve the mutual understanding of both sides," said Alexei Karyakin, a representative of the insurgents in the Luhansk region.
In Moscow, the Kremlin said Putin underlined in his conversation with Obama that to normalize the situation in eastern Ukraine, it's necessary to "effectively end fighting and start direct talks between the conflicting parties."
White House spokesman Josh Earnest said Obama urged Putin to use his personal influence with the separatists to promote peace and stability in Ukraine, stop backing the insurgents and halt the flow of arms across the border. Earnest said that while the U.S. believes a diplomatic solution to the crisis is still possible, "Russia will face additional costs if we do not see concrete actions to de-escalate the situation."
Ukraine and the West have accused Russia of fomenting the rebellion in the east by sending troops and weapons across the border. Moscow has denied that and insisted that Russian citizens who joined the insurgents were volunteers.
Poroshenko's office said Monday that he has offered Russia a chance to send its own observers to join the OSCE mission in Ukraine to see that government troops were observing the cease-fire.
Monday's talks involved Ukraine's ex-President Leonid Kuchma, the Russian ambassador to Ukraine and an envoy from the OSCE. Poroshenko has ruled out talks with those he calls "terrorists," so inviting Kuchma to mediate offered a way to conduct talks without the government's formal engagement.
Kuchma, who served as president from 1994 to 2005, comes from the east and is an astute political player respected by both sides. His ex-chief of staff, Viktor Medvedchuk, has lived in Russia and reportedly has close ties to Putin, was also at the talks.
If both sides observe the cease-fire, "then a normal peace process could start," Kuchma told reporters after Monday's talks.
Poroshenko's deputy chief of staff, Valeryi Chalyi, said in televised remarks that Monday's talks were a "move in the right direction."
Russian Ambassador to Ukraine, Mikhail Zurabov, voiced hope that the talks would ensure a "lasting truce" and the "launch of an inclusive negotiation process."
Putin publicly expressed support Sunday for Ukraine's declaration of a cease-fire and urged both sides to negotiate a compromise, which, he said, must guarantee the rights of the Russian-speaking residents of eastern Ukraine.
Putin clearly intends to maintain pressure on the Ukrainian government in Kiev to give the country's eastern industrial regions more powers, which would allow them to keep close ties with Russia and serve the Kremlin's main goal of preventing Ukraine from joining NATO.
But the Russian leader also wants to avoid more crippling sanctions from the U.S. and particularly from the European Union, whose leaders will meet Friday in Brussels, and therefore needs to be seen as cooperating with efforts to de-escalate the conflict.
Isachenkov reported from Moscow.
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