Algerian President Tebboune underlined that"The BRICS interest us" as an alternative to traditional power centers, he said in a televised interview late Sunday. "They constitute an economic and political force."
The president said there was no need to "get ahead of things" but promised "good news."
Tebboune's comment comes after Russian President Vladimir Putin -- whose country is hit with Western sanctions over its Ukraine invasion -- in June called on BRICS leaders to move towards "formation of a truly multipolar system of inter-government relations."
The BRICS group also includes the major emerging economies of Brazil, India and South Africa.
BRICS members currently account for nearly a quarter of the world's gross domestic product.
Tebboune participated in a BRICS virtual summit at the end of June, when Putin called on leaders of the group to cooperate in the face of "selfish actions" from the West.
On a visit to Algeria in May, Russian Foreign Minister Sergei Lavrov said trade between his country and Algeria had reached $3 billion last year.
Sanctions over Ukraine have pushed Putin to seek new markets and strengthen ties with countries in Africa and Asia.
Algiers abstained when the United Nations General Assembly overwhelmingly passed a resolution in March demanding Russia immediately withdraw from Ukraine.
China, India and South Africa also abstained.