Oil producers within and outside the OPEC cartel last week agreed to extend a November accord to cut crude production by nine months in a move spearheaded by Moscow and Riyadh.
"We are grateful to you for your ideas and joint work on the combined steps by OPEC members and non-members," Putin told 31-year-old Prince Mohammed, who is the country's defence minister, the Interfax news agency reported.
"The actions we agreed are helping to stabilise the situation on the world hydrocarbon markets."
Putin told Prince Mohammed that Moscow and Riyadh "together were working on the issues of resolving difficult situations, including in Syria."
Prince Mohammed's meeting with Putin comes shortly after US President Donald Trump visited Riyadh as part of his first overseas trip.
Putin again reiterated an invitation for Saudi monarch King Salman to visit Russia and insisted it would be a "good sign and a good signal.