The announcement came yesterday after local media and social media reports on Monday said at least four senior military officers had been arrested, information that was not immediately confirmed by the Niger authorities.
"The government has foiled an unfortunate attempt to destabilise our institutions," Issoufou said in his annual address on the eve of the country's independence celebrations.
There was no immediate reaction from the opposition in the impoverished former French colony.
"The main authors behind this crazy plot have all been identified and arrested, with the exception of a single person who is on the run," the president said.
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"The situation is calm and under control. The ongoing inquiry will allow us to identify the other actors and possible accomplices," he said.
"The aim of these individuals, driven by an unknown motivation, was to overthrow democratically elected institutions," he added, notably through the use of "aerial firepower".
The president had announced the thwarting of another coup plot in a similar message to the nation in 2011. Ten military figures were arrested at the time, accused of attempting to overthrow the regime and "attempted assassination of the head of state".