July 2 (Reuters) - Oil production at the Karachaganak field in Kazakhstan has been restored amid rising natural gas output and increasing supplies to a drone-hit Russian gas plant across the border, an industry source said on Thursday.

Kazakhstan cut gas production at its Karachaganak oil and gas condensate field after Ukraine's drone attack on the Orenburg gas processing plant in Russia on June 24.

Oil and gas output at Karachaganak are closely linked, meaning the field is not able to produce much oil if its gas production is down.

The ministry, in emailed comments, said gas supplies to the plant had resumed already on June 26, and the gas has been flowing at 290,000 cubic metres per hour, which is still below normal volumes.

Kazakhstan's Energy Minister Erlan ​Akkenzhenov said earlier on Thursday that the gas supplies are at 28% of the usual levels.

Raw gas from Karachaganak, whose stakeholders include Chevron CVX.N and Shell SHEL.L, is usually delivered across the border to the Orenburg plant.

The source said oil production at the field by July 1 increased to 33,000 metric tons per day, ot 259,100 barrels per day. For the whole June, it reached 976,500 tons, below the planned 984,000 tons.

Energy ministry did not reply to a request for comment on oil production at Karachaganak.

The plant was also hit last October.

In addition to Chevron and Shell, Karachaganak's stakeholders include Italy's Eni ENI.MI, Russia's Lukoil LKOH.MM and local firm KazMunayGas KMGZ.KZ.

Ukraine has said its campaign of long-range drone strikes on Russian energy facilities aims to weaken a key source of military funding and bring the conflict closer to home for Russians.

President Vladimir Putin has said such attacks on civilian infrastructure are intended to sow discord among the population.