Six people were injured when two blasts went off at a market in the Abkhaz capital Sukhumi on Monday, a day after six people were injured by two bombs in Abkhazia's Black Sea resort of Gagra.
"We are seriously concerned over the news of explosions on June 29 and 30 in the cities of Gagra and Sukhumi," the ministry said. "According to our information, there were no Russian tourists among the injured."
Abkhazian President Sergei Bagapsh said earlier Monday that starting Tuesday the republic would close its border with Georgia, which he said was behind the blasts.
"From tomorrow, the Georgian-Abkhaz border will close," Bagapsh said. "We know where it all comes from - from Georgia. Having tried everything, they [Georgian authorities] have resorted to the most disgraceful thing - terrorist attacks."
Sergei Shamba, the foreign minister of Abkhazia, reiterated that the blasts were organized by Tbilisi and said the border would remain closed until the end of the tourist season.
"The closure of the border is only a temporary measure as we want to guarantee safety for tourists as well as for our citizens," Shamba said. "We have no doubt that the recent blasts in Sukhumi and Gagra were organized by Georgian special services."
Georgia denies the allegations, saying the blasts could be the result of turf wars between various criminal groups operating in the unrecognized republic.
"This is not a serious statement," Georgian Defense Minister David Kezerashvili said. "We have repeatedly said that it [Abkhazia] is an uncontrolled territory where criminal groups are operating."
"I would advise the Abkhaz authorities to put their house in order," he said.
Abkhazia broke away from Georgia in the early 1990s following the collapse of the Soviet Union. Between 10,000 and 30,000 people were killed in the subsequent fighting.
The pro-Western government of Georgian President Mikheil Saakashvili has said it is determined to bring the breakaway region back under Tbilisi's control.