By Alexander Tanas

CHISINAU (Reuters) - Authorities in Moldova's separatist Transdniestria region ended month-long power cuts and began restoring heat to apartments in wintry conditions on Monday as flows of natural gas resumed, funded by the European Union.

Transdniestria, which split from Moldova at the end of the Soviet era, had relied on Russian gas passing through Ukraine, but Kyiv refused to extend a transit deal beyond the New Year, saying it helped fund Moscow's nearly three-year-old invasion.

Moldovan energy company Moldovagaz shipped the first batch of 3 million cubic metres (mcm) of natural gas on Saturday to the Russian-backed separatist enclave.

"The priority now is starting up the heating system," Vadim Krasnoselsky, Transndniestria's self-styled president, told reporters.

"We have to raise the temperature in the central heating system so that residents get heat in their homes. The rolling blackouts have been stopped."

Krasnoselsky expressed gratitude to the head of the EU's Executive Commission, Ursula von der Leyen, for providing the 64 million euros ($65.9 million) in funding for the gas supplies.

He also offered unusual thanks to Moldovan specialists for overseeing delivery of the gas to guard against the pipeline system losing pressure entirely.

Residents expressed relief at a return to normal daily life in the region of 350,000, where Russian "peacekeepers" remain in place more than three decades after a brief conflict between the separatists and the newly independent Moldovan state.

"Not everyone has hot water yet, but at least there is heat, gas and electricity," Olga, 38, told Reuters from the main regional city of Tiraspol.

"I no longer have to run around the city to find power so I can work remotely. My older daughter goes back to school tomorrow, but they still have to get the heating going in my younger daughter's school."

The EU funding is intended to provide gas for Transdniestria's needs for the first 10 days of February, with no arrangements yet in place beyond that. Krasnoselsky said the available gas had to be used "with the maximum efficiency".

Energocom, the government gas distribution company, has been purchasing gas for Transdniestia on European markets - about 3 mcm per day - since Saturday.

Some of the EU funds are to be used by government-controlled Moldova to provide electricity for its own residents.

Moldova has relied on a thermal plant in the separatist region to provide cheap power, but determined it was more economical to buy power from suppliers in European countries.

Gas supplies have long been a source of tension between Russia and Moldova, which lies between Ukraine and Romania.

After Ukraine refused to renew the transit deal, Moldova asked Russian giant Gazprom to provide gas through alternative routes, mainly Turkey.

Gazprom said Moldova first had to settle arrears it estimated at $709 million, a figure contested by Chisinau.

(Reporting by Alexander Tanas, Writing by Ron Popeski; Editing by Marguerita Choy)