The report came during a visit by Saudi King Salman to Moscow.
He stressed that Saudi Arabia has already held talks with a dozen Russian energy companies and has certain developments, projects, plans for cooperation.
The pact on cutting output by about 1.8 million barrels per day (bpd) took effect in January this year.
"We emphasise that the security and stability of the Gulf region and the Middle East is an urgent necessity for achieving stability and security in Yemen", the king said.
The president stressed that Russian Federation is perfectly aware of the concerns of regional countries, including Iran, Turkey and Saudi Arabia. The agreement remains in force until the end of March 2018.
But prices are still half their mid-2014 levels.
Luton-based Monarch Airlines cancels all flights after falling into administration
Your stories will help our journalists have a more complete picture of these events and we will use them in our reporting. Transport secretary Chris Grayling said the collapse of the firm was the result of a recent price war between airlines.
The two also diverge on Yemen, where a Saudi-led coalition military intervention in the country has killed more than 10,000 people since 2015, drawing criticism from Moscow and the worldwide community.
Russian Federation and Saudi Arabia have clinched a number of lucrative deals as King Salman paid the first official visit to Russian Federation by a Saudi monarch.
Earlier in the day, King Salman met with the Russian leader to discuss a number of issues, including the oil market situation, defense industry cooperation, situation in Syria and the diplomatic rift between a number of Arab states and Qatar.
The commentator further pointed out to Russia's willingness to establish contacts with all sides in the Middle East in order to find solutions for regional problems.
Saudi Foreign Minister Adel al Jubeir also said that the two countries are working to unite Syrian opposition and that they have agreed on the need to preserve Syria's territorial integrity and state institutions.
Saudi Arabia is now investing over $1 billion in over 20 Russian projects including the construction of a petrochemical complex and Pulkovo Airport in St Petersburg, Russian Energy Minister and co-chairman of the Russian-Saudi Intergovernmental Commission Alexander Novak said.
Russian Federation is not a member of the oil cartel Opec, but it has collaborated with Opec members on suppressing production to drive up oil prices.