Mikhalkov in July, 2000, at a Moscow film festival, wearing a "Hero of Socialist Labor Golden Star," one of the highest Soviet awards.
"He died of old age. He simply fell asleep," said his grandson, film producer Yegor Konchalovsky, RIA-Novosti reported.
President Dmitry Medvedev and Prime Minister Vladimir Putin offered condolences to his family, including his two sons, prominent film directors Oscar-winning Nikita Mikhalkov and Andrei Konchalovsky.
Both of his sons were abroad at the time of his death, news reports said.
Mikhalkov was hospitalized after suffering from a heart attack in February but celebrated his 96th birthday the next month back home with his family.
Born in Moscow on March 13, 1913, Mikhalkov wrote his first lyrics at the age of 9 and published his first song in 1928 in a Rostov-on-Don literature magazine, the poet wrote in his 1995 autobiography "I Was a Soviet Writer."
He rose to national prominence in 1935 with the publication of his popular children's book "Uncle Styopa," known as "Uncle Steeple" in the English version. The book is a simple rhythmic poem about an extra-tall Muscovite who becomes a police officer and carries out a series of charitable and heroic deeds, one after another.
But it was not "Uncle Styopa," beloved by generations of children born in the Soviet Union and translated into 40 languages, that made Mikhalkov famous.
In 1936, Mikhalkov won a powerful patron in Soviet leader Josef Stalin, who liked a poem titled "Svetlana" that he had published that year, Mikhalkov recalled in a 2008 interview with Izvestia.
"I was young then and dated a student who was elder than me. Her name was Svetlana," Mikhalkov said. "But everyone decided that the poem was about Stalin's daughter," also named Svetlana.
In 1938, Mikhalkov was ushered into the prestigious Writer's Union, which he headed from 1970 until his death, and the following year he was awarded his first of four Orders of Lenin, for satirical poems and fables.
In 1944, Stalin decided to replace "The Internationale," the socialist anthem by French poet Eugene Pottiere, as the Soviet anthem and picked lyrics written by Mikhalkov and poet Gabriel El-Registan and set to music by Alexander Alexandrov. Mikhalkov loved to relate in television interviews how he received drafts of his lyrics back from Stalin, marked with Stalin's suggestions and changes.
A line from the anthem — about Stalin inspiring and raising "us" for labor and heroic deeds — is inscribed on a wall in the newly restored Kurskaya metro station, drawing ire from human rights activists.
For more than 20 years after Stalin's death, the anthem was performed without lyrics, until Mikhalkov replaced references to Stalin with Lenin in 1977. This anthem remained unchanged until 1993, when then-President Boris Yeltsin introduced a new wordless anthem based on a patriotic song by Mikhail Glinka.
In 2000, then-President Vladimir Putin controversially reintroduced the Soviet anthem, and Mikhalkov rewrote the lyrics again. Mikhalkov described the new lyrics as "the anthem of an Orthodox Christian nation." The words describe the vastness and grandeur of Russia and do not mention any national leaders by name.
Mikhalkov faced scorn from literature critics and by some of his peers for putting his talent to work for the Soviet authorities and for showing loyalty to whoever was in charge in the Kremlin. He also participated in smear campaigns against "anti-Soviet" authors such as Nobel laureates Boris Pasternak and Alexander Solzhenitsyn.
But Mikhalkov denied being subservient to the Communist Party. "I have never been influenced by politics," he told Kommersant in 2003. "I always served the state."
Mikhalkov also wrote the well-known phrase inscribed on the Tomb of the Unknown Soldier next to the Kremlin and on many similar monuments across the country: "Your name is unknown, your deed is immortal."
In 1962, Mikhalkov created a short satirical movie newsreel, "Fitil," or "Fuse," that preceded most movie performances in Soviet times. More than 600 "Fitil" shorts were produced under his leadership over 45 years.
A funeral for Mikhalkov will be held at the Christ the Savior Cathedral on Saturday, said an aide to his son Nikita Mikhalkov, Interfax reported.
He will most likely be buried at Novodevichoye Cemetery, where his first wife, Natalya Konchalovskaya, is buried, a source close to the Mikhalkov family told Interfax.
Nikita Mikhalkov's "Burnt by the Sun" about a family during the Stalinist purges won the Academy Award for Best Foreign Picture in 1994. Andrei Konchalovsky's films include the Oscar-nominated "Runaway Train" and "Tango & Cash."
Mikhalkov is also survived by his physicist wife, Yulia Subbotina, 10 grandchildren and eight great grandchildren.