The attacks, on Sunday and Monday, claimed a total of 34 lives.
Thousands of police are patrolling public transport and checking traffic in the city following the attacks, which injured some 60 people.
The first victim has been buried – a policeman killed at the train station.
No group has said it carried out the attacks, which Russian investigators believe are connected. 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.
Reserves called in
The bombing of the railway station on Sunday and the attack on a trolleybus on Monday came days before the New Year holiday – one of Russia’s biggest celebrations – and just over a month before the opening of the Winter Olympics in Sochi.
In a New Year address in the eastern city of Khabarovsk, Mr Putin said: “We bow our heads in front of the victims of the terrible acts of terror.
“We will fiercely and consistently continue the fight against terrorists until their complete annihilation.”
More than 5,000 officers were deployed on Tuesday morning, regional security spokesman Andrei Pilipchuk said.
Extra reserves and the “maximum number of police and interior ministry soldiers possible” were being brought in, he said.
As many as 600 police officers from the city were recently transferred to Sochi, 688km (428 miles) to the south-west, to help with preparation for the Games which begin on 7 February, Reuters news agency reports.
Events for New Year’s Eve, such as children’s parties, have been cancelled in the city, while residents have been asked not to set off fireworks.
The death toll rose overnight as a person wounded in Sunday’s attack on the station died of their injuries, bringing the total fatalities in that attack to 18.
Another person injured in Monday’s attack on a trolleybus also died, bringing that toll to 16.
The first victim to be buried on New Year’s Eve was transport policeman Dmitry Makovkin, 29, killed at a metal detector in the station, where the suicide bomber set off the device.
Hundreds of mourners attended the funeral. His commander hailed Mr Makovkin as a hero who possibly prevented greater loss of life by preventing attackers from entering the station.
A second victim was being buried on Tuesday and funerals are due to continue through the holiday period.
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.
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