"Vladimir Putin expressed deep condolences to the family and relatives of Yevgeny Primakov over his death," the Kremlin said in a statement.
"He was a statesman, scientist, politician, he has left behind a great legacy," Kremlin spokesman Dmitry Peskov told reporters.
A veteran of Soviet and Russian politics, Primakov served as premier under president Boris Yeltsin in 1998-1999.
He was installed in the top government job amid political and economic turmoil after Russia defaulted on August 17, 1998.
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Considered one of the country's foremost experts on the Middle East, he was also a member of the Kremlin's security council until 1999.
During the 1991 coup he refused to support Communist hardliners and sided with Mikhail Gorbachev.
Known for aggressively standing up for Russia's interests, Primakov is most vividly remembered for ordering his US-bound plane to turn around over the Atlantic after he learned from Al Gore, his US counterpart at the time, that NATO had begun a bombing campaign against Yugoslavia in 1999.
At the time, Primakov was accused of single-handedly putting Russia on the path of confrontation with the West.
"Primakov has turned around Russia," broadsheet daily Kommersant wrote at the time.
Senior ruling United Russia party lawmaker Vladimir Vasilyev said it was Primakov who promoted the idea of a "bipolar world" and Russia's closer ties with major developing economies China and India.
Some saw Primakov as a possible successor to Yeltsin.
But he was sacked in May 1999 -- two months after the famous plane episode --- as Yeltsin began to fear Primakov's alliance with Yury Luzhkov, Moscow's powerful mayor at the time, experts said.
State news agency RIA Novosti called Primakov a "crisis manager".
"In the 1990s Primakov managed to save the SVR and the foreign ministry and then to pull Russia out of the economic spin," it said.