Dignitaries led by President Vladimir Putin paid their last respects to the former prime minister, whose remains lay in state in the House of Unions in central Moscow flanked by an honour guard.
"Without doubt he was a great citizen of our country," Putin said after laying flowers by the coffin and briefly touching it with his hand.
"His authority was indisputable abroad. He was always the centre of attraction for many people. People talked to him, consulted him, compared notes with him. I can say this is also entirely true about me.
Top dignitaries including Prime Minister Dmitry Medvedev and US ambassador John Tefft filed by the coffin, an array of Primakov's medals laid flat on velvet cushions in front of the casket.
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After the civil ceremony Primakov's body was taken to the 16th-century Novodevichy Monastery where the head of the Russian Orthodox Church Patriarch Kirill conducted the funeral service as officials looked on, clutching lit candles.
He is to be buried at the adjoining cemetery later in the day.
Primakov, who passed away Friday at the age of 85, was considered the last of the Soviet-era political giants.
He is perhaps most vividly remembered for turning around his US-bound plane over the Atlantic after learning of NATO's bombing of Serbia in 1999.
The cancellation of the US visit is widely considered a turning point in Russia's foreign policy after Moscow's rapprochement with Washington following the collapse of the Soviet Union.
"Serbia will always remember what could not be forgotten, that in its most difficult moments he was a great and proven friend," Serbian Foreign Minister Ivica Dacic said on Friday.
A fluent Arabic speaker and one of the country's foremost experts on the Middle East, he personally knew Iraq's Saddam Hussein, Moamer Kadhafi of Libya and Hafez al-Assad of Syria.