Pierre Nkurunziza flew back from a summit in Tanzania, but the airport had been closed to stop him from landing. His plane reportedly returned to Tanzania.
Heavy fighting has been taking place overnight between soldiers loyal to the president and those who back the coup.
Confusion remains as to whether the coup has been successful or not.
Burundi coup was announced by Maj. Gen. Godefroid Niyombare, a former intelligence chief and ally of the president who was dismissed in February, after Pierre Nkurunziza left for Tanzania on May 13.
Thousands of people took to the streets to celebrate the announcement.
However, overnight, army chief of staff Gen. Prime Niyongabo – a supporter of President Pierre Nkurunziza – announced: “The attempted coup… has been stopped.”
His announcement came after a night of negotiations between Gen. Prime Niyongabo and the defense minister, who backs the coup.
Factions loyal to each side began fighting each other for control of the national television and radio station, witnesses said.
There has been mounting unrest in Burundi since President Pierre Nkurunziza, who came to power in 2005, announced he was seeking a third term in office – apparently in contravention of the constitution.
Announcing the coup, Gen. Godefroid Niyombare said he did not recognize the leadership because the president’s bid for a third term violated the constitution.
“The masses vigorously and tenaciously reject President Nkurunziza’s third-term mandate. President Pierre Nkurunziza has been relieved of his duties. The government is overthrown,” he said in a radio broadcast.
A few hours later the Burundi presidency dismissed the coup attempt, saying: “It is with regret that we have learned that a group from the armed forces mutinied this morning and declared an imaginary coup.
“This coup attempt has been foiled and that these people, who read the coup announcement on the radio, are being hunted by defense and security forces so that they can be brought to justice.”
Pierre Nkurunziza had been in Dar es Salaam to discuss the crisis with regional leaders.
He flew back to Burundi upon learning of the coup, but the airport had been shut to prevent him landing, and so he had returned to Dar es Salaam. It is not clear if he remains there.
Tanzanian President Jakaya Kikwete said the summit had condemned the coup, adding: “The region will not accept, nor will the region stand by, if violence does not stop or escalates in Burundi.”
The US and UN have appealed for calm.
Burundi unrest began on April 26 and has led to the deaths of more than 20 people.
Tens of thousands of Burundians have fled to neighboring states in recent weeks.
President Pierre Nkurunziza has rejected calls to postpone next month’s election. However, the summit in Tanzania urged him to do so.
Pierre Nkurunziza, a 51-year-old former rebel leader, argues that he is entitled to run for a third term because he was first appointed to the role by parliament in 2005.
The Burundian constitution states a president should govern only for two terms, but earlier this month a court upheld Pierre Nkurunziza’s interpretation.
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