Mourners and commuters on Moscow's metro describe the affect of the attacks
Russian Prime Minister Vladimir Putin says investigators should view catching the organisers of Monday's suicide attacks as a "matter of honour".
He said the security services, who have been widely criticised in the media, should drag the bombing masterminds "from the bottom of the sewers".
On Tuesday, Russians observed a day of mourning for 39 people killed in the attacks on two Moscow Metro trains.
Officials have blamed the bombings on militants from the North Caucasus.
Russian media reports are linking the attacks to the death of a rebel leader from Ingushetia - Alexander Tikhomirov, also called Said Buryatsky.
He was killed by Russian security forces earlier this month after being blamed for an attack on a train last year in which 26 people died.
Russian newspaper Kommersant quoted investigation sources as saying they believed Tikhomirov had recruited 30 suicide attackers from Ingushetia and neighbouring Chechnya.
Police fear that two of the bombers he trained might have blown up the Moscow trains to avenge his death, according to reports.
The BBC's Richard Galpin in Moscow says the main concern for Russia is whether Monday's bombings were the start of a new wave of attacks by rebels.
Security has been stepped up in the capital, as police are reported to be searching for three people sighted with the bombers.
The Metro is back up and running, but commuters say the city was not yet back to normal.
"I feel the tension on the Metro. Nobody's smiling or laughing," university student Alina Tsaritova told the Associated Press news agency.
The authorities say two female suicide bombers detonated explosives packed with pieces of metal.
MOSCOW METRO ATTACKS
March 2010: Two suicide bombers blow themselves up at Lubyanka station and Park Kultury station, killing 39 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
Russian newspapers have published pictures of two dead women, purported to be the suicide attackers.
In the early 2000s, Russian cities were hit by attacks by women from the Caucasus known as "black widows" because their husbands were believed to have been killed by Russian soldiers.
Russian media have also published a CCTV image they say is a man suspected by police of helping in the attacks.
In a meeting with senior officials, Mr Putin urged investigators to find the organisers.
"We know they're lying low, but it's a matter of honour for law enforcement bodies to scrape them from the bottom of the sewers and into the daylight," he said.
Much of Mr Putin's political reputation was built on his tough stance against rebels from Chechnya while he was president.
His successor as president, Dmitry Medvedev, said the government would consider revamping anti-terrorism laws to try to prevent further attacks.
Some of the families of the victims have been expressing anger at their loss.
The grandmother of Valya Yegeazaryan, 17, who died in hospital after the explosion at Park Kultury station, questioned what the authorities were doing to tackle militants.
Extra security measures are in place on Moscow's metro system
"I cannot get my child back. There have been so many terrorist attacks, and yet what what have [the authorities] done?" asked Valentina Yegeazaryan.
"Some time passes, and then the same thing happens again."
Mourners lit candles and laid flowers at the sites of the blasts - the Lubyanka and Park Kultury stations.
As well as the 39 killed, some 70 people are reported to still be in hospital - some of whom are seriously hurt.
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.
The city's Metro is one of the busiest underground rail networks in the world, carrying about 5.5 million passengers a day.
Chechen rebel leader Doku Umarov vowed last month to take the war to Russian cities.
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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