Speaking on Monday, Putin said that while trade ties with Mali were "modest" there was an upward trend and future areas of cooperation would be in "geological exploration, energy, logistics and the humanitarian field".
Mali and Russia have previously discussed the construction of a Russian-designed nuclear power plant as a strategic energy project for Mali.
"This official visit will contribute to further deepening our relationship in a spirit of mutual trust and respect for sovereignty," Col Goïta said, according to a statement by the Malian presidency.
Goïta expressed gratitude for Russia's "warm welcome" and affirmed Mali's willingness to strengthen the cooperation, which he said "covers many sectors".
Military cooperation remains a key element of the Russia-Mali alliance.
Russian mercenary forces have supported Col Goïta's government since French and UN troops were expelled after years of counterinsurgency operations.
The Wagner Group recently withdrew from the country, but another force, the Africa Corps, remains.
When the army seized power in Mali, it cited the need to contain a deteriorating security situation as a major reason for the coup.
However violence has worsened in recent years despite promises to deal with the conflict.
Russian Defence Minister Andrei Belousov, who held separate talks with his Malian counterpart Sadio Camara, said the priority of the Russia-Mali partnership was "to achieve practical results in enhancing security and sovereignty".
"This approach is the key to any success and victory," the AFP news agency quoted him as saying.
