He said further decisions on fuel market regulation would be published in the near future.
Despite being one of the world's top oil producers, Russia has suffered shortages of gasoline and diesel in recent months as high export prices made it advantageous for refiners to sell their products abroad.
Kommersant reported that the ban would be lifted only on pipeline exports of diesel, and that volumes may be subject to quotas to avoid surges in wholesale prices.
The ban on gasoline exports will remain in force for now, it said.
Diesel is Russia's biggest oil product export, at almost 35 million tonnes last year. It exported 4.8 million tonnes of gasoline.
The newspaper said Deputy Prime Minister Alexander Novak was due to hold a weekly meeting later on Wednesday with oil companies to discuss the possible easing of the ban.
Novak's office did not immediately reply to a request for comment.
Novak said last week that Russia may introduce quotas on fuel exports if a complete ban on cross-border supplies imposed on Sept. 21 does not succeed in bringing down high gasoline and diesel prices.
Prices have fallen on the local exchange since the ban was introduced; gasoline by almost 10%, and diesel by 23%.
The oil pipeline monopoly Transneft's storage facilities are nearly full and it is proving almost impossible to redirect all incoming volumes to the domestic market, Kommersant said.
On Tuesday, Novak said the government was not setting any time frame for the fuel export ban.
Analysts' expectations vary on how long the measures will be in effect. JP Morgan said it could last a couple of weeks until harvest season concludes in October, while FGE Energy said replenishing Russia's gasoline stocks could take up to two months.
(Reporting by Lidia Kelly in Melbourne and Vladimir Soldatkin in Moscow; Editing by Simon Cameron-Moore, Kim Coghill and Kevin Liffey)
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