(CNN) -- Russian President Vladimir Putin paid a New Year's Day hospital visit to some of those injured in two suspected suicide bombings in the city of Volgograd.
More than 30 people were killed in the attacks on Sunday and Monday at a rail station and on a trolley bus, just six weeks before Russia is due to host the Winter Olympics.
Putin's unannounced visit to Volgograd Wednesday came a day after he delivered a New Year's message on Russian state TV in which he vowed to fight until terrorists were defeated.
He met with regional security and police officials in the city, the state-run RIA Novosti news agency reported.
"The abomination of this crime, that was -- or crimes -- that were committed here, in Volgograd, don't need any additional commentary," Putin said.
"No matter what motivated the criminals' actions, there is no justification for committing crimes against civilians, especially against women and children."
Putin then laid flowers at the scene of Monday's attack, RIA Novosti said, before visiting a hospital to meet men and women undergoing treatment for their injuries.
The blasts in Volgograd intensified fears of terrorism following a threat earlier this year from a Chechen extremist group to use "maximum force" to disrupt the February Olympic games in Sochi.
No group has claimed responsibility for the attacks, described as suspected suicide bombings.
In his address Tuesday, Putin acknowledged problems in 2013 but said the Russian people had a lot to look forward to in 2014. He also had a message for terrorists.
"We bow our heads to the victims of violent terrorist attacks. We will continue the fight against terrorists certainly, fiercely and consistently until their complete annihilation," he said.
While security in Sochi and its surrounding area is considered to be very tight, the attacks in Volgograd, a major transportation hub for southern Russia, have raised concerns about the potential vulnerability of other areas of the country.
Volgograd is a main transit point for people traveling by train to Sochi, a Black Sea resort situated just over 400 miles (645 kilometers) to the southwest.
The death toll from the two attacks rose to 34 Tuesday when some of those hurt died from their injuries, state media reported.
The number of people killed in an explosion at the Volgograd's main rail station Sunday now stands at 18, RIA Novosti said, citing the Emergencies Ministry. Another 16 died following the blast on a trolleybus during the morning rush hour Monday, the news agency said, attributing the information to health officials.
There was a strong security presence in Volgograd for the city's New Year's Eve celebrations.
More than 3,000 police and dozens of volunteers were on the streets overnight, the state-run Itar-Tass news agency reported, citing the local branch of Russia's Interior Ministry.
Russian police earlier detained dozens of people in an anti-terror sweep in the city. It wasn't clear if any of those held had any suspected connection to the attacks or would face any charges.
International Olympic Committee President Thomas Bach voiced his confidence in Russia's ability "to deliver safe and secure Games in Sochi" in a letter to Putin Monday.
In what appeared to be a public relations offensive designed to improve his country's image ahead of the Winter Olympics, Putin introduced a sweeping amnesty law last month.
Among those to benefit were two members of Russian punk band Pussy Riot, who were allowed to leave prison.
The amnesty also freed 28 protesters and two journalists who were thrown in prison after being arrested in September aboard a Greenpeace ship as they protested against drilling for fossil fuels in the Arctic.
Putin also pardoned former oil tycoon and Kremlin critic Mikhail Khodorkovsky, who had been jailed since 2003 and was convicted in 2005 of tax evasion and fraud.
The Russian president has also faced international criticism over anti-gay legislation passed in July that banned "propaganda of nontraditional sexual relations around minors."
In an apparent jab at the anti-gay laws, the United States announced that its delegation to the Winter Olympics would include openly gay athletes such as tennis legend Billie Jean King and hockey player Caitlin Cahow.
CNN's Jethro Mullen contributed to this report.