The Children's Circle Dance fountain on Privokzalnaya Square seen outside a damaged train station following a suicide attack in Volgograd, on December 29, 2013.

President Vladimir Putin warned that Russia would "continue to fight against terrorists until their total destruction" on Tuesday.

In a New Year's address from the Russian city of Khabarovsk, Putin remembered the victims of the recent bombings in the southern city of Volgograd, saying, "Dear friends, we bow our heads in front of the victims of the terrible acts of terror."

"In the current year, we have encountered problems and have been challenged by serious experiences, including ones like the inhuman acts of terror in Volgograd," Putin was quoted as saying by Russian news agencies.

The country began mourning its dead, as the toll from Sunday and Monday's bombings rose to 34.

Volgograd began burying those killed in Sunday's attack on the city's main railway station, while the toll from Monday's attack on a trolleybus climbed to 16.

More from GlobalPost: Why Volgograd?

The attacks come just six weeks before the start of the Winter Olympics in Sochi, located around 425 miles southwest of Volgograd.

Putin ordered heightened security at public transportation hubs around the country, while more than 5,000 law enforcement officers monitored the streets and railways in Volgograd.

Experts fear that the attacks are a test of security ahead of the Sochi games.

"I don’t want to believe that somebody else will repeat this in January and February," Alexey Malashenko, scholar in residence at the Carnegie Endowment for International Peace's Moscow office, told NBC News. "But it is possible that Islamist extremists will try to show that they are able to do everything on the territory of the Russian Federation."

Another concern is that while security resources are diverted to guard Sochi, attacks could take place in other cities in Russia.

While no one has claimed responsibility for the Volgograd attacks, Chechen rebel leader Doku Umarov urged his fighters in July to use "any means possible" to disrupt the Sochi games.

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