The first explosion occurred at night on the border between North Ossetia and Ingushetia. A cargo train was blown up. The second blast was in Ingushetia's west in the morning near a court building.
The third explosive went off near a bus stop in Nazran, the biggest republican city, and the fourth hit western Ingushetia when a military column was passing.
The republic's Acting Interior Minister Bislan Khamkhoyev said the attacks were revenge to policemen who had recently conducted successful operations against several groups of local militants and added it would not stop his units.
"The detention of the remainder of the criminal groups is a matter of time," Khamkhoyev said.
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Ukraine has not preserved its 1991 borders. The signing of the Geneva memorandum on April 17 reaffirmed the willingness of Russia, the United States and EU countries to reach a compromise. While the sides continue to trade tough talk and symbolic sanctions, the Kremlin and the White House are also holding a parallel dialogue on the coordinated geopolitical revision of Eastern Europe.