DONETSK Ukraine (Reuters) - Fresh volleys of artillery fire were heard across many parts of the separatist stronghold of Donetsk in eastern Ukraine on Sunday, a Ukrainian government statement said, after Kiev warned again of rebel preparations for a fresh offensive.

A Reuters witness in central Donetsk heard several dozen blasts of artillery fire, although it was unclear who had launched them or what was under attack.

Shelling from both sides has repeatedly punctured a ceasefire, agreed in a deal signed on Sept. 5 to end a war that has killed more than 4,000 people since April. Government forces and rebels have accused each other of violating the terms of the truce, raising fears it could collapse entirely.

A government statement issued in the name of Donetsk city administration said the situation in the city was tense.

"According to residents, powerful volleys and explosions of heavy weapons can be heard in many districts," it said

Ukraine's pro-Western leaders and NATO have accused Russia of sending soldiers and weapons to help pro-Russian rebels launch a possible new offensive, a charge the Kremlin has repeatedly denied.

Before the latest reports of shelling, a Ukrainian military spokesman said on Sunday the weekend had been calmer than in previous days, but warned again of a buildup in separatist forces.

"Compared with previous days, the number and intensity (of shelling) fell, but there are signs of rebels and Russian forces preparing for an offensive," Andriy Lysenko said in a briefing in Kiev.

In separatist Luhansk region, three members of Ukraine's special police force were killed as a result of a rebel attempt to break into Ukrainian-controlled territory, the Interior Ministry said in an online statement. The press service for the military operation said another soldier had been killed elsewhere in the region.

Andrei Purgin, deputy prime minister of the self-proclaimed 'Donetsk People's Republic', told Reuters rebels had reached an agreement with Ukrainian forces to stop shelling around Donetsk airport following a meeting that included representatives of Russia and security watchdog OSCE.

Ukrainian military spokesman Lysenko said he did not have information on the agreement referred to by Purgin. U.S. President Barack Obama said on Sunday that Russia would remain isolated by the international community if President Vladimir Putin failed to end Russian backing for separatist rebels in Ukraine.