The talks were held on Thursday with the participation of other Russian and Saudi officials.
“We have held detailed talks behind closed doors to talk about bilateral relations and the situation in the region,” Putin said after the meeting. “That was a very meaningful, substantive and confidential conversation.”
The Russian president also said he was confident the visit by Salman would give a fresh impetus to the development of bilateral ties with Riyadh. Putin also accepted an invitation by the Saudi king to Saudi Arabia.
Salman and his delegation arrived in the Russian capital for a four-day visit on Wednesday.
The Saudis have reportedly signed more than 15 cooperation agreements — with multi-billion-dollar energy and military contracts — with the Russian side. Moscow has also agreed to sell its advanced S-400 missile defense system to Riyadh.
Putin and Salman also discussed the conflict in Syria, where they support opposing sides. The Saudis have been backing the wide range of militants fighting the elected Syrian government, while Russia backs the legitimate Damascus government.
Saudi Arabia has officially been calling for an ouster of Assad, while Russia says the future of Syria and the political future of Assad should only be determined by the Syrian people.
Nevertheless, Salman claimed that Riyadh favors a political solution to the conflict in Syria, according to a report by TASS.
“A political solution must be achieved that would guarantee security, stability, unity and territorial integrity of Syria,” he was quoted as saying.
The two leaders also discussed the oil market and how to stabilize prices.