Falih said that Saudi Arabia wants to develop ties with Russian Federation further, particularly in the private sector.
Oil traded near $50 a barrel in NY as traders weighed a flood of USA crude exports against the possibility of extended production cuts by OPEC and Russian Federation.
Saudi Arabian King Salman bin Abdul Aziz harshly criticised Iran on his first visit to Russian Federation, which has close relations with the Islamic republic.
Ties between the two countries were often strained in the past.
Matviyenko expressed her hope that King Salman's visit would be successful and fruitful, and would give a strong impetus to the development of bilateral relations.
This is also the first time in recent years, according to SIPRI, that Saudi Arabia has purchased weaponry from Moscow, as the United States is Riyadh's main source of arms.
Monitoring oil exports may add another layer of support to the OPEC-led effort to balance an oversupplied market, a director at a vessel tracking firm said.
She also expressed her gratitude to the Saudi foreign minister for his cooperation with Moscow, especially with his Russian counterpart Sergei Lavrov.
"We aim to strengthen our relations in the interests of peace and security, in the interests of developing the world economy", the Saudi king responded, according to AFP news agency.
At the same time, Saudi Arabia continues to present itself as a regional and global player that is indispensable. However, any discord was eclipsed by mutual expressions of respect, and the pomp and ceremony laid on by Russian officials to greet the Saudi king. "But you shouldn't think it's forever".
Earlier, Russia invited Turkmenistan to join the OPEC oil output cut deal.
The two countries helped secure a deal between OPEC and other producers to cut output until the end of March 2018, but back competing sides in Syria's civil war.
"We strive to continue the positive cooperation between our countries to achieve stability on world oil markets which promotes the growth of the world's economy", Salman said.
"Today, the King of Saudi Arabia went to Moscow, and at the same time, the president of Turkey went to Tehran, to Iran. But on the whole, if speaking about a possible extension, this should be at least until the end of 2018".
"These delays are not critical, there is nothing awful there, but as I have always said ... it is the most hard thing to resolve tasks at a final stage", Putin said at a meeting with senior sports officials, regional governors and prominent athletes to discuss preparations for next year's tournament.