But a Western diplomat told CNN that gunfire could be heard in Bujumbura, the capital of the African nation.
President Pierre Nkurunziza is out of the country, attending a crisis summit with other East African leaders in Tanzania.
When contacted by CNN, Burundian government spokesman Willy Nyamitwe said reports of a coup were "a joke."
A statement from the President's office said some soldiers had mutinied and declared an "imaginary" coup.
The statement appealed for calm, said the coup attempt had been foiled, and added that those responsible "are being sought by defense and security forces so that they are brought to justice."
According to Reuters, Army Gen. Godefroid Niyombareh announced on radio earlier in the day that Nkurunziza has been "dismissed" and that a national salvation committee had been set up to run the country. CNN has not been able to independently confirm whether the coup attempt has been successful or has been foiled.
Niyombareh is the former head of Burundian intelligence. He was fired by the President in February.
Celebrations in the streets
The news that Nkurunziza might have been deposed is being greeted with jubiliation, Nsengiyumva Pierre Claver, a former member of an EU electoral monitoring team, told CNN by phone from Bujumbura.
"We have observed many people just shouting of joy and dancing in the streets," Claver said. People had come from areas in the hills surrounding the capital to join in the celebrations, he said.
And soldiers had been able to reopen two private radio stations that had been closed by the government, he said.
But Claver, too, had heard reports of gunfire -- near the national radio and TV stations, he said -- and he warned it was too soon to conclude that the coup attempt had been successful.
Nkurunziza has been seeking a third term, something prohibited by the agreement that ended the country's 1993-2003 civil war. Protesters determined to prevent his candidacy have demonstrated in Bujumbura, the capital, and have been met with deadly force by police.
About 300,000 people died in Burundi's 10-year, ethnically driven civil war. And Burundi is a neighbor of Rwanda, where in 1994 an estimated 800,000 minority Tutsis and moderate Hutus were slaughtered in an ethnic genocide.
Burundi, like Rwanda, has a Hutu majority and a Tutsi minority. While the current crisis is rooted in politics, some observers have feared that the government might try to stoke ethnic animosities in a last-ditch effort to retain power.