Mobile phone access was partially restored in war-torn eastern Ukraine on Friday after it was lost more than a week ago, the last major Ukrainian provider in the area said.

Almost two million people lost mobile connection in the devastated region after a Vodafone Ukraine fibre optic line was cut on January 11 as a result of fighting.

The provider sought to restore service after its workers had received security assurances from the warring parties in a conflict that has claimed more than 10,000 lives in nearly four years.

"Repair work on the restoration of communications... is completed. In the Lugansk region, communication services are provided in full," Vodafone Ukraine said in its statement, referring to the smaller of two breakaway provinces.

Meanwhile, the insurgent-controlled parts of the bigger Donetsk region still remain without a mobile connection.

"In the Donetsk region, the network does not work for reasons unknown to us. There is a possibility that the equipment is out of order or there is no power supply," Vodafone added.

The separatist authorities of the self-proclaimed Lugansk republic confirmed the restoration of mobile phone access as Donetsk leaders declared no changes in the area under their control.

The outage all but severed communication between family members living on opposite sides of the frontline splitting eastern Ukraine.

Russian-backed operator Pheonix, now the sole provider in Donetsk, only this week introduced a service that is theoretically able to place calls to Kiev-controlled regions at international rates.

The departure of Ukraine's KyivStar in 2015 and Lifecell last year left Vodafone as the only major provider in the region of some 3.5 million people.

This has left Phoenix filling the void in Donetsk, but it has only 600,000 subscribers and is already operating at full capacity.

The self-declared "communications minister" of Donetsk, Viktor Yashchenko, told the separatist DAN news agency earlier this week that 80,000 people had joined Phoenix since Vodafone went down.