KIEV, Jan 29 (Reuters) - Three Ukrainian servicemen were killed when pro-Russian rebels attacked government positions in Avdiyivka on Sunday, cutting off power supplies to the eastern frontline town, Ukrainian officials said.

The two-year-old Minsk peace agreement has failed to stop fighting in eastern Ukraine with each side accusing the other of violating the terms of a ceasefire on a near-daily basis.

Ukrainian military spokesman Oleksandr Motuzyanyk said troops had repelled an early-morning attack by rebels seeking to storm their positions in Avdiyivka's industrial zone.

"The situation remains very tense. The enemy continues to fire artillery and mortars at our positions, although it is not on the offensive for now. Ukrainian troops along the whole front line are in a state of higher alert," he said in a regular daily briefing.

The latest shelling also left much of Avdiyivka, which had a pre-conflict population of around 35,000, without electricity as of 1130 GMT, the news agency Interfax Ukraine quoted local official Pavlo Malykhin as saying.

As a result, only one of four power feeds at Avdiyivka Coking Plant - one of Europe's largest producers of fuel for the steelmaking industry - is currently running, chief executive Musa Magomedov said on Facebook.

Meanwhile separatist officials said Ukrainian forces had fired from tanks and artillery more than 900 times at rebel positions on the other side of the front line near Avdiyivka.

One rebel fighter was killed and another wounded, separatist website DAN reported.

Close to 10,000 people have been killed since fighting between Ukrainian troops and rebels seeking independence from Kiev erupted in April 2014.

Kiev and NATO accuse the Kremlin of supporting the rebels with troops and weapons and the United States and the European Union have imposed sanctions on Russia over the conflict, as well as for its annexation of Crimea.

The latest clashes come ahead of a visit by President Petro Poroshenko to Berlin on Monday to discuss the state of the conflict with Chancellor Angela Merkel, who helped broker the much-violated Minsk peace deal.

Kiev is anxious that international resolve to hold Russia to account not waver following the inauguration of U.S. President Donald Trump. Trump has expressed a desire to improve ties with Moscow and spoken of possibly lifting sanctions.

(Reporting by Alessandra Prentice; editing by Ralph Boulton)