"It's become dangerous to ride the Metro but I'll keep taking the Metro. You have to get to school, to college, to work somehow."
Lighted candles and flowers have been left in memory of the victims of the blast inside the Lubyanka station, where at least 23 people died, and the Park Kultury station, where the second explosion killed at least 12 people.
Richard Galpin BBC News, Moscow
Millions of commuters are running the gauntlet on board the Moscow Metro fully aware of what happened 24 hours ago. They are doing so on what is an official day of mourning in memory of those killed and injured on Monday.
Although security has now been stepped up on the Metro and, for example, at airports, the big concern is that what happened on Monday was just the start of a new wave of attacks by rebels from the North Caucasus region.
The self-proclaimed leader of the militants has pledged to bring the war to mainland Russia. The question is whether the security forces can now gather sufficient intelligence to prevent any further attacks.
Another four people died in hospital, and officials have warned that the death toll could rise.
The main television channels have changed their schedules, dropping advertising and entertainment programmes.
Prime Minister Vladimir Putin, visiting the injured at a hospital in Moscow, said law enforcement agencies would "do everything to find and punish the criminals".
Mr Medvedev laid a wreath at the scene of one of the attacks on Monday. He called the plotters "beasts", adding: "We will find and destroy them all."
Russian Foreign Minister Sergei Lavrov told the Interfax news agency that militants operating on the Afghan-Pakistan border may have helped organise the Moscow attacks.
"We all know very well that clandestine terrorists are very active on the border between Afghanistan and Pakistan," he was quoted as saying.
"We know that several attacks have been prepared there, to be carried out not only in Afghanistan, but also in other countries. Sometimes, these journeys go as far as the (Russian) Caucasus."
Russia's leaders paid respects to Metro victims
US President Barack Obama pledged that Washington would "help bring to justice those who undertook this attack" while Secretary of State Hillary Clinton called terrorism a "common enemy".
Other foreign ministers from the G8 group of leading industrial nations also condemned the attacks at the start of talks on global security in Ottawa, Canada.
Finger of blame
Police are looking for two women who accompanied the bombers as well as a possible male accomplice, after identifying them and the bombers through surveillance footage, security sources were quoted as saying by Russian media.
MOSCOW METRO ATTACKS
March 2010: Two suicide bombers blow themselves up at Lubyanka station and Park Kultury station, killing 38 people
August 2004: Suicide bomber blows herself up outside Rizhskaya station, killing 10
February 2004: Suicide bombing on Zamoskvoretskaya line, linking main airports, kills 40
August 2000: Bomb in pedestrian tunnel leading to Tverskaya station kills 13
February 2000: Blast injures 20 inside Belorusskaya station
January 1998: Three injured by blast at Tretyakovskaya station
June 1996: Bomb on the Serpukhovskaya line kills four
The head of Russia's intelligence service, the Federal Security Service (FSB), said investigators believed the attacks had been carried out by "terrorist groups related to the North Caucasus".
"Fragments of the bodies of two female suicide bombers were found earlier at the scene of the incident and examinations show that these individuals came from the North Caucasus region," Alexander Bortnikov said.
The co-ordinated attacks were the deadliest in Moscow since February 2004, when 40 people were killed by a bomb on a packed metro train as it approached the Paveletskaya station.
Six months later, a suicide bomber blew herself up outside another station, killing 10 people. Both attacks were blamed on rebels from Chechnya.
Chechen rebel leader Doku Umarov claimed responsibility for that attack and vowed last month to take the war to Russian cities.
Chechnya's Kremlin-backed leader Ramzan Kadyrov condemned the attacks in Moscow, saying he would assist the Kremlin in hunting down the culprits.
More than 100,000 people have been killed in 15 years of conflict in Chechnya, and low-level insurgencies continue there and in the neighbouring republics of Ingushetia and Dagestan.
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