A homemade bomb exploded at a racetrack in Nalchik on Saturday, killing one person and wounding at least 20, rescue workers said.
Emergency Situations Ministry duty officer Marat Prokopenkov said the bomb exploded near a VIP box during a horse race in the capital of Kabardino-Balkaria.
The man who died was identified as a World War II veteran born in 1906.
No one immediately claimed responsibility for Saturday's bombing, which occurred as Russia celebrated May Day.
The bomb was equipped with a timer and filled with pieces of metal designed to injure as many people as possible, said regional Interior Ministry spokeswoman Marina Kyasova.
The leaders of the republic, including President Arsen Kanokov, were not at the racetrack.
"[The blast] could be revenge by extremists for the destruction of the leaders of bandit groups and could be aimed at destabilizing the situation in the republic during May holidays," Kanokov said, Itar-Tass reported.
In the neighboring republic of Ingushetia, a man was shot dead by policemen after opening fire at a sports complex, Interior Ministry spokeswoman Madina Khadziyeva said.
The man opened fire after policemen began to search him at the entrance to the sports complex in the city of Nazran, where the Ingush leader and other officials were attending a national judo competition, the spokeswoman said.
Ingush President Yunus-Bek Yevkurov barely survived an assassination attempt last year.
The identity of the dead gunman was not immediately clear, Khadziyeva said.
(AP, Reuters)