He added that consultation between the Kingdom and Russian Federation is continuing and is considered constructive in all fields and that "we are confident that the two countries would contribute to bringing about security, peace and stability to the region and the world at large".
But relations have been improving between the two nations with an energy pact forged a year ago when 24-oil exporting countries, including Saudi Arabia and Russian Federation - the two largest oil exporting nations - agreed to cut output to halt the downward drift of the oil price.
During the Cold War, the Saudis helped arm Afghan rebels fighting against the Soviet occupation.
Members of OPEC, of which Saudi Arabia is the biggest producer, have joined with non-member Russian Federation and other countries in cutting crude output in a pact that has helped prop up prices.
The visit comes a month before members of the OPEC oil cartel, of which Saudi Arabia is the biggest producer, are due to meet with the other nations that have joined them in cutting crude output, including Russian Federation, to discuss extending the pact that has helped prop up prices.
So far, that deal is holding.
The two countries also signed a series of multi-billion dollar investment deals including one to create a $1 billion fund to pursue energy projects. Mr Putin expressed hope that it would boost ties between the two countries.
Saudi King Salman's visit to Russian Federation "is a historical one" as it shows that "the two parties are ready to open a new era", Hassan Nafaa said.
Shiite powerhouse Iran and Sunni-majority Saudi Arabia are regional foes. More recently, tensions were high over the war in Syria.
"We have held detailed talks behind closed doors to talk about bilateral relations and the situation in the region", TASS quoted Putin as saying.
Moreover, RDIF and Saudi Arabia's sovereign fund Public Investment Fund (PIF) plan to invest in more than 25 projects in the areas of consumer goods production, agriculture, real estate, infrastructure, oil and gas sector, TASS reported.
Moreover, the talks between the leaders of the two countries could contribute to the settlement of the Middle Eastern crisis, the expert argued.
While Russia has said Kurds have the "right" to declare independence, Iran has joined Saudi Arabia, Iraq, Turkey, and Syria in opposing Kurdistan's efforts to become a sovereign nation.
Putin and Salman also discussed the conflict in Syria, where they support opposing sides.
Saudi Arabia and Russian Federation are heavily dependent on oil exports and the plunge of the price of crude that began in 2014 lashed both of their economies. It has entered into a deal with Ukraine to manufacture its AN-130 in Saudi Arabia and expects similar deals with other countries. USA light crude was up 10 cents at $50.08.