KIEV, Oct. 9 - Ukraine's military on Sunday postponed a planned parallel withdrawal with pro-Russian separatists from Stanytsa Luhanska, a town on the eastern frontline, saying rebels had disregarded the agreement by firing artillery at Ukrainian positions, Reuters reported.

In September, the two sides agreed a pilot de-escalation project in three small towns - part of a push to revive a much-violated ceasefire and end a conflict that has killed over 9,600 since early 2014.

"The separation of forces and equipment which was planned for today was postponed," said General Borys Kremenetsky, Ukraine's representative to the ceasefire coordination center.

"The main reason is the continuation of shelling along the line of separation. I would say there has been an increase over the last few days and use of heavy artillery," he told journalists.

The delay is yet another setback for the struggling peace process. Both sides accuse the other of violating the 18-month-old 'Minsk' ceasefire agreement on a near-daily basis.

On Sunday, Ukrainian military spokesman Andriy Lysenko said rebels had used heavy artillery in a "major" attack in part of the Luhansk region. Meanwhile separatist officials accused Ukrainian troops of firing at a rebel-held residential district in southern Donetsk region, separatist news site DAN reported.

Nevertheless, both sides have said they have withdrawn from Petrovske in Donetsk region and Zolote in Luhansk region - the other two areas listed in the latest de-escalation pact.

The Organization for Security and Cooperation in Europe, which monitors the implementation of the ceasefire, said on Saturday its monitors had witnessed the movement of troops and equipment out of the Petrovske area, but could not yet confirm if a full withdrawal had taken place there.

While limited in geographic scope - the areas are each four kilometers squared - the disengagement agreement is the first time the sides have said they would withdraw light arms. High-caliber weapons are already meant to have been withdrawn to secure holding areas, although the OSCE regularly reports violations on both sides.

In Stanytsa Luhanska, locals appeared skeptical of the success of the withdrawal plan.

"I think the majority disagree with it. We don't believe them, because it always happened that when they had to observe the truce they never did. Why do you think they will respect the demilitarized zone?," resident Galina told Reuters, declining to give her last name. (rt/ez)