Five million tonnes of oil were contaminated last month with organic chloride and some of the dirty crude is still stuck in pipelines in Belarus and eastern Europe.
Russia has managed to take out around 2 million tonnes of the tainted oil from the pipeline system and agreed with Belarus last week to take back another 1 million tonnes.
Two industry sources told Reuters on Monday that Russia's oil exports via Transneft pipelines, including Druzhba, dropped 6% during May 1-26 from the average level seen in April.
The country's oil production over the same period totalled 11.126 million barrels per day (bpd), down from 11.147 million bpd on May 1-21, the sources said.
Russia's recent oil output is below the 11.18 billion bpd target Moscow has pledged as part of an international deal among producers to curb production to support prices.
The oil contamination crisis, along with reduced exports from OPEC members Iran and Venezuela following US sanctions on both countries, have lifted global oil prices.
Russia's energy ministry, which oversees the energy data collection, declined to comment. So far, Russia has managed to restore some flows to Belarus, Ukraine and Slovakia.
On Monday, Czech pipeline operator MERO said that oil shipments via the Druzhba pipeline to the Czech Republic restarted at noon (1000 GMT).
Belarus state energy company Belneftekhim said on Monday that Belarus began pumping contaminated oil towards Russia on Friday and by the end of Sunday it had pumped 80,000 tonnes of it back to Russia.
Belarus Mozyr oil refinery is working at planned capacity while the Novopolotsk oil refinery is still operating at reduced capacity after the Druzhba oil contamination, Belneftekhim said.
Following high-level talks in Moscow last week, Belarusian Prime Minister Sergei Rumas said that Russia had confirmed it was ready to pay compensation for damages incurred as a result of the oil contamination.