According to analysts, the Kremlin could strengthen its position in the region by pushing Armenia, another close ally, towards compromise on the issue.
Medvedev was present for the talks, which were held at his residence in Barvikha near Moscow.
An enclave of Azerbaijan with a largely ethnic Armenian population, Nagorny Karabakh broke free of Baku's control in the early 1990s in a war that killed nearly 30,000 people and forced two million to flee their homes.
A ceasefire was signed in 1994 but the dispute remains unresolved after years of negotiations.
Shootings between Armenian and Azerbaijani forces in the region are common.
In October, Medvedev launched a fresh push to end the conflict during a visit to Armenia.
At the meeting, Sarkisian said he was ready for talks with Azerbaijan on the basis of principles worked out at negotiations in Madrid last year under a plan that would give Nagorny Karabakh the right to self-determination.
The Kremlin would act as guarantor of a new accord, an administration official was quoted as saying on Saturday.
"Russia would be prepared to support a resolution to the problem that suits both sides and act as guarantor if a compromise deal is reached," the unnamed Kremlin official said, according to state news agency RIA Novosti.
A resolution would also "allow the return of stability and calm in the South Caucasus and in the post-conflict period maintain the historical balance of power in the region".