Russian President Vladimir Putin has described the recent suicide attacks in Volgograd as "indefensible", during a visit to the city.
"No matter how the criminals may justify their actions, there is no justification for crimes committed against civilians," he said.
The bombings - one at the main railway station and the other on a city trolleybus - killed 34 people.
Security has now been increased, and thousands of police have been deployed.
No group has said it carried out the attacks, but analysts say the bombings could have been an effort to derail the Winter Olympics in Sochi, which begin next month.
They are similar to previous indiscriminate attacks by Islamist militants operating from the North Caucasus.
Volgograd, a city of one million known as Stalingrad during World War II, commemorated the 70th anniversary of the battle of the same name this year, in an outpouring of Russian patriotic fervour.
Investigators believe a male suicide attacker bombed the trolleybus and are studying fragments of his body in an effort to identify him. Police sources say the attack on the station may also have been the work of a male bomber.
Identical shrapnel was used in the bombs, according to Vladimir Markin, spokesman for Russia's Investigative Committee.
Analysts say the prime suspect for the attack is likely to be Doku Umarov, a fugitive Islamist militant leader from Chechnya.
He has orchestrated previous bomb attacks on Russian civilian targets, and vowed in July that his fighters would use "any means possible" to keep Mr Putin from staging the Sochi Games.