MOSCOW, April 20 (Reuters) - Russia's energy and finance ministries have agreed to reduce fuel tax from May 1, cutting 350 billion roubles ($4.5 billion) from the state budget in 2021-2023, they said on Tuesday.

The finance ministry said earlier in April that Russia planned to tackle rising fuel costs by changing taxes and paying more compensation to companies for holding down prices.

To offset half of the budget losses, the government will hike the mineral extraction tax (MET) on oil production, the ministries added in their statement.

They said the higher extraction tax would not have a significant negative effect on Russian oil companies' earnings.

The rising price of gasoline is a sensitive issue for the authorities, who have struggled to stick to their pledges to cap it at the current rate of inflation.

($1 = 76.8310 roubles) (Reporting by Olesya Astakhova and Darya Korsunskaya. Writing by Polina Devitt and Vladimir Soldatkin. Editing by Mark Potter)