This is the first visit to Moscow by a reigning Saudi Monarch.
Riyadh on Thursday signed a preliminary agreement to buy S-400 air defence systems from Russian Federation, the Saudi military industries firm said.
"King Salman does not do courtesy calls so it can be reasonably assumed that his first official visit to the Russian capital is a serious event", wrote Chris Weafer, a senior partner at Macro-Advisory, a consultancy.
Russian authorities, the academic said, are trying to show "a new opening" in dealing with the Middle East developments.
On Tuesday, Putin had said that Russian Federation is ready to cooperate with the United States on the basis of equality.
"I think the market is trying to stabilize", said Gene McGillian, director of market research at Tradition Energy.
The two countries have already struck a deal on weapons sales and leaders discussed the oil market and Syrian crisis.
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The relationship, which involves coordinated production cuts to eliminate an oversupply and joint energy investments, brings both short- and long-term gains, he said after a meeting in Moscow with his Russian counterpart Alexander Novak.
Reports say the deals range from an arms deal worth $3bn (£2.3bn) to a $1bn energy investment fund.
Speaking alongside Lavrov, Saudi Foreign Minister Adel al-Jubeir said that Moscow and Riyadh agreed on the need to preserve Syria's territorial integrity.
The OPEC deal was aimed at reducing a global oil glut that had seen crude prices plummet from over 100 dollars a barrel in 2014 to a 13-year low of under 30 dollars last year.
Saudi Arabia's King Salman bin Abdulaziz Al Saud gets off the plane upon his arrival at Moscow's Vnukovo Airport on October 4, 2017.
Beyond short-term market drivers, analysts at Barclays said future oil demand could be undermined by improving fuel-efficiency and the rise of electric vehicles (EV). The Riyadh Administration, which is converging on Russian Federation, aims to diversify its diplomatic relations and reduce dependence on United States, while key players in region develop strong partnerships with Turkey and Iran, a challenging process to conduct Moscow with Saudi Arabia Waiting.
A slew of investment agreements would be signed during King Salman's trip and plans for a $1-billion fund to invest in energy projects are likely to be finalised then, as part of efforts by two of the world's biggest oil producers to expand cooperation.