government document showed on Monday.
It also lifted restrictions on the export of fuel already accepted for export by the Russian Railways and Transneft before the initial ban was announced last week.
The ban on all types of gasoline and high-quality diesel remains in place.
Russia announced on Thursday that it had temporarily banned exports of gasoline and diesel to all countries outside a circle of four ex-Soviet states with immediate effect in order to stabilise the domestic market.
In recent months, Russia has suffered shortages of gasoline and diesel. Wholesale fuel prices have spiked, although retail prices are capped to try to curb them in line with official inflation.
The crunch has been especially painful in some parts of Russia's southern breadbasket, where fuel is crucial for gathering the harvest.