Russia's investigative committee said it was looking into the causes of the accident. It said, however, there was no suspicion of a militant attack, the cause for scores of deaths in Moscow's underground in years past.
Injured passengers were carried on stretchers, bloodied and bandaged, out of metro stations and helicopters ferried the most seriously hurt to hospital. Passengers looked stunned or were crying after being helped to the surface by emergency services.
"There is no one alive left," Moscow's deputy mayor Peter Biryukov said. "The cause is not known, the work continues."
Biryukov said three bodies were recovered from the wreckage, but that some bodies remained underground.
Russia's Itar-Tass news agency cited the Emergencies Ministry as saying 19 had died in the accident.
Investigators said earlier a power surge caused the train to stall and several cars to come off the rails between the Slaviansky Boulevard and Park Pobedy stations.
"It braked very hard. The lights went off and there was lots of smoke," a man, his nose bloodied, told Rossiya-24 television.
"We were trapped and only got out by some miracle. I thought it was the end. Many people were hurt, mostly in the first rail car because the cars ran into each other."
A city transport services spokesman told news agency Interfax that all passengers had been evacuated from the affected stations by midday, dismissing reports that some passengers were still trapped in the underground tunnel.
The Moscow metro is the world's busiest, with as many as 9 million people on week days riding a system that is widely recognized for its reliability.
Famed for its high-vaulted halls adorned with Soviet socialist realist art, the underground network has expanded from 13 stations opened in 1935 to 194 stations across the megalopolis today.
Islamist militants have previously carried out deadly attacks in Moscow, including twin suicide bombings that killed 40 people on the subway in 2010.
(Reporting by Andrey Kuzmin and Tatiana Ustinova, Writing by Alissa de Carbonnel and Lidia Kelly, Editing by Ralph Boulton)