A government document showed on Monday that the Russian government agreed to some amendments to the fuel export ban, lifting restrictions on fuel used to supply some ships, and diesel that contains a high percentage of sulfur.
Moscow also lifted restrictions on the export of fuel that Russian Railways and Transneft had previously agreed to export before the initial ban was announced last week.
The ban on all high-quality gasoline and diesel remains in effect.
Russia announced on Thursday that it had temporarily banned gasoline and diesel exports to all countries except four former Soviet countries, with the decision taking effect immediately to achieve stability in the local market.
In the past few months, Russia has suffered from a shortage of gasoline and diesel. Wholesale fuel prices rose, although retail prices were capped in an attempt to keep them in line with the official inflation rate.
The crisis was most severe in some parts of the breadbasket region of southern Russia, where fuel is needed to collect crops.
This may constitute a serious and embarrassing crisis for the Kremlin as the presidential elections approach next March.