Russian Prime Minister Vladimir Putin says catching the organisers of suicide bombings in Moscow on Monday should be a "matter of honour" for investigators.
He said the security services, who have been widely criticised in the media, should drag the bombing masterminds "from the bottom of the sewers".
Russians are observing a day of mourning for 39 people killed in the rush-hour attacks on two Metro trains.
Officials have blamed the bombings on militants from the North Caucasus.
Moscow says the main concern for Russia is whether Monday's bombings were the start of a new wave of attacks by rebels.
No group has claimed responsibility, but previous attacks in the capital have been carried out by - or blamed on - militants from Chechnya.
Security has been stepped up in Moscow, 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 said.
The authorities say two female suicide bombers detonated bombs packed with pieces of metal at two separate stations during rush hour on Monday morning.
In a meeting with senior officials, Mr Putin urged investigators to find the organisers of the attacks.
"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 in a bid 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 a hospital after the explosion at Park Kultury station, questioned what the authorities were doing to tackle militants.
"I cannot get my child back. There have been so many terrorist attacks, and yet what what have [the authorities] done?" said Valentina Yegeazaryan.
"Some time passes, and then the same thing happens again."
Meanwhile, mourners have been lighting candles and laying 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.
US President Barack Obama led international reaction to the attacks, saying Washington would "help bring to justice those who undertook this attack".
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.
Security sources told Russian media that police were looking for two women and a man they suspected of helping the bombers.
The sources said the suspects had been identified through surveillance footage.
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 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.
The city's Metro is one of the busiest underground rail networks in the world, carrying about 5.5 million passengers a day.