"This is a huge loss for the entire human rights movement in Russia," the council's head Mikhail Fedotov said in a statement.
She died around 1630 GMT Saturday evening in a Moscow hospital, he said.
"It was not the first time that she was in this hospital, doctors had already revived her several times in the most difficult of situations. But there are situations in which doctors can do nothing." Russia's rights ombudswoman Tatiana Moskalkova mourned her loss.
"For those who have appreciated democracy in the past, for those who appreciate it now, and those who will appreciate it in the future, Lyudmila Mikhaylovna has always been and will always be a symbol of honesty and the uncompromising struggle for human rights," she said.
Alexeyeva tirelessly defended human rights from the 1950s in the Soviet Union right up to recent years under strongman leader Vladimir Putin.
In 1976 she was one of the founders of the Moscow Helsinki Group, whose members were arrested, jailed or forced into exile over the years.
She continued to defend Soviet dissidents when she herself was forced into exile, living in the United States until returning in 1993 after the fall of the USSR.
In recent years her fight went on, as she tried to shed light on the fate of Sergei Magnitsky, who died in prison after accusing Russian officials of tax fraud, and denounced the imprisonment of anti-Kremlin tycoon Mikhail Khodorkovsky.
In 2009 the European parliament awarded her the prestigious Sakharov Prize, along with the Memorial human rights group. (AFP) SCY
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