* Rebel truce runs parallel to Ukraine forces ceasefire
* No fighting reported on ground for first time in weeks
* Talks with rebels involved Moscow envoy
* EU urges Russia to use influence on separatists (Adds background, context)
By Aleksandar Vasovic
DONETSK, Ukraine, June 23 (Reuters) - Separatist leaders in two main areas of Ukraine's east have agreed to observe a ceasefire with Ukrainian forces until June 27, one of them, Alexander Boroday, said on Monday.
The truce is to run parallel to a unilateral Ukrainian military ceasefire declared by President Petro Poroshenko on Friday as part of a peace plan to end the insurgency by pro-Russian separatists in the Russian-speaking east that threatens the dismemberment of the former Soviet republic.
The separatists' announcement, after talks which also involved a senior Russian diplomat and a former Ukrainian president, came after a day of high diplomacy in which the West urged Russia to use its influence to defuse the conflict in Ukraine's rebellious east.
Speaking after meeting a "contact group" which included a representative of the OSCE security watchdog, Boroday said: "The consultation ended with authorities of the Luhansk and Donetsk Republics agreeing to maintain a ceasefire for their part ...until the 27th."
An unusual lack of armed incidents throughout Monday, making it the first non-violent day in the east for weeks, appeared to indicate that the rebels had begun to observe their truce earlier in the day.
Volodymyr Chepovy, an official of Ukraine's National Security and Defence Council, said that from 9 a.m. to 5 p.m. no incidents of weapons use were recorded. "There were no attempts to seize administrative buildings or military points etc."
Ukrainian ex-president Leonid Kuchma, who took part in the talks, said the agreement on a two-way ceasefire until 10 a.m. on June 27 meant "one of the key problems has been resolved."
The declaration of a rebel ceasefire after talks involving a Russian representative seemed certain to be welcomed by the West as a sign Moscow could be ready now to help engineer a settlement in Ukraine's troubled east.
Andriy Parubiy, head of Ukraine's National Security and Defence Council, said the participants at Monday's talks had also agreed there should be cooperation to free hostages.
Earlier, the European Union, with whom Ukraine will sign a landmark association and trade agreement on Friday, threw its weight behind Poroshenko's peace initiative after hearing a report from his new foreign minister, and it urged Russia to use its influence on the separatists to halt the violence.
"The EU calls on all sides to agree and honour a ceasefire immediately in order to stabilise the security situation, achieve a genuine de-escalation and create the necessary conditions for President Poroshenko's peace plan to be implemented," the EU bloc said in a statement in Luxembourg.
Though Poroshenko announced his ceasefire last Friday, Kiev reported a spate of armed attacks by rebels on Ukrainian military and border posts over the weekend.
Scores of people have been killed and wounded in Ukraine since the rebellions erupted in the industrial east in April following the toppling of the Moscow-backed president Viktor Yanukovich by protesters in February and Russia's subsequent annexation of the Russian-majority Crimea region.
The dead include about 150 Ukrainian servicemen - among them 49 who died when a cargo plane was brought down by rebel fire - and scores of rebels and ordinary citizens.
It has been the worst bloodshed in Ukraine since it became independent with the breakup of the Soviet Union in 1991.
Russia has denied Kiev's charges that it has helped foment the separatist unrest and knowingly allowed military equipment to cross into Ukraine or built up forces along the 1,900 km (1,190 mile) joint border.
While Russian President Vladimir Putin at the weekend gave qualified support for the pro-Western Poroshenko's peace plan he urged Kiev to hold a dialogue with the "opposing side" and find a compromise.
Poroshenko has refused direct talks with separatists who control strategic buildings and points in the main industrial city of Donetsk and the towns of Luhansk and Slaviansk.
Declaring a week-long ceasefire for Ukrainian forces last Friday, he told the rebels, who have declared "people's republics" and said they want to join Russia, to use the time to lay down their arms or face a Ukrainian offensive in a "plan B".
But the inclusion of Kuchma, a long-serving Ukrainian ex-president in Monday's talks with a rebel leader, appeared to be a sign that Poroshenko was trying to meet Putin halfway in his demand for dialogue with the separatists.
Shortly after the rebel ceasefire was announced, the Kremlin said Putin had addressed Ukraine with U.S. President Barack Obama in a telephone conversation on Monday.
"They discussed ... the implementation of the peace plan proposed by President Petro Poroshenko. Putin stressed that priority must be given to halting military operations and to the start of direct negotiations," the Kremlin said.
(Additional reporting by Alissa de Carbonnel in Moscow; Writing By Richard Balmforth and Alessandra Prentice; Editing by Mark Heinrich)