Russia stepped up security nationwide on Monday after two blasts in the southern city of Volgograd left at least 32 people dead and score of others injured.

The United Nations, China, the United States and many other members of the international community have condemned the terrorist attacks and pledged joint efforts to fight terrorism.

Russian President Vladimir Putin ordered the National Anti-Terrorism Committee to tighten security throughout the country. The committee said several presidential instructions were specially on Volgograd, some 900 km southeast of Moscow.

However, no extra security measures will be adopted for the upcoming Sochi Winter Olympic Games, Russian Olympic Committee President Alexander Zhukov told reporters.

"As for the Olympics, all necessary security measures have been taken. No additional security measures will be taken in Sochi ... Everything necessary has been done," he said.

The 22nd Winter Olympic Games, the first to be held in Russia, are slated for February 7-23 with 98 sets of medals up for grabs. Volgograd is some 690 km northeast of Sochi.

On Sunday, a suicide bomber ripped a railway station in Volgograd, killing 17 people and injuring 45 others. Another bomb went off Monday morning in a trolley bus on the same city, leaving at least 15 dead and 28 others wounded.

The two explosions have drawn immediate international condemnation.

UN Secretary-General Ban Ki-moon was appalled by the twin bombings, a UN spokesperson said Monday. In a telephone conversation with Putin, Ban stressed the importance of strong international cooperation to the fight against terrorism and noted that perpetrators must be brought to justice.

Putin urged the international community to work together in the fight against terrorism and commended the United Nations for its important role in coordinating efforts in combating organized crime and terrorism.

Also on Monday, the UN Security Council strongly condemned the attacks, saying it is "outraged" by two suicide bombings taking place in the same Russian city within a 24-hour period.

Chinese Foreign Minister Wang Yi and his Russian counterpart, Sergei Lavrov, held a phone conversation to exchange views on the serial blasts. Wang strongly denounced the terror attacks, saying China supports the measures taken by Russia to safeguard national security and stability.

Meanwhile, the United States also denounced the twin terrorist attacks and voiced hope for "closer cooperation" with Russia in its security arrangements for the upcoming Sochi Olympics.

Other members of the international community, including the European Union, the Shanghai Cooperation Organization, Azerbaijan, Georgia, Slovenia and Syria, have also condemned the attacks.

"The entire Olympic Movement joins me in utterly condemning this cowardly act," International Olympic Committee President Thomas Bach said in a letter to Putin.

The attacks in Volgograd were unable to undermine the confidence that Russia could guarantee security of the upcoming Sochi Winter Olympics, he added.