The two presidents witnessed the signing of more than a dozen agreements covering military, oil and gas, education and health care cooperation.
Sang said he and Putin had fruitful talks to bring relations between the countries forward.
"In the atmosphere of openness and trust, we exchanged views on bilateral relations and agreed on measures to further strengthen and expand the comprehensive strategic partnership between Vietnam and Russia," Sang told reporters.
In an article carried by state media on Monday, Putin wrote, "Russian-Vietnamese friendship has stood the test of time, having lived through the numerous tragic events of the 20th century and drastic changes in the world as well as in our countries."
Vietnam and Russia were close ideological allies until the break-up of the former Soviet Union in 1991. Bilateral relations warmed up after Putin first became president, and the countries signed a strategic partnership agreement in 2001.
Cooperation in energy has gone beyond the oil and gas sector. Russia's state atomic energy corporation, Rosatom, has been awarded the rights to build Vietnam's first nuclear power plant.
Putin was to travel to South Korea later Tuesday.