Tensions have been high in the country ever since Tandja pushed through a constitutional reform that allowed him to stay in office after his term expired in December.
On Thursday morning, a series of loud explosions and bursts of automatic gunfire were heard in Niamey.
Witnesses said shooting began at about 12pm GMT and appeared to be centred on the presidential palace. Smoke was seen coming from the palace and soldiers were deployed around it.
Later, people reported seeing the bodies of at least three soldiers being lifted out of a an armoured vehicle that stopped outside a morgue.
RFI correspondent Lydia Addo says she tried to go to the main mortuary in the city but she was stopped by troops. She had been told that a number of dead soldiers had been brought there.
She says that by about 3.45 GMT the situation in the city had calmed but was still very tense.
Trade union leader Moustapha Abubakar told RFI on Thursday afternoon that no official announcements had been made by either the government, the opposition or the military.
France asked French citizens living in the country to stay indoors.
State radio carried no information on the events but began playing music by the Niger military band at around 5.40pm GMT. Three previous coup announcements in Niger over the past thirty years have been preceded by similar music.
Tandja has been in power for over a decade and extended his term thanks to a controversial referendum last August.
The Nigerien President’s actions drew widespread criticism and led to international sanctions. West African regional bloc Ecowas suspended Niger’s membership while the European Union and the United States also imposed sanctions.
At an Ecowas meeting in Abuja, Nigeria on Tuesday, leaders urged everyone involved in the interim administration not to put themselves up as candidates in the next elections. Talks aimed at ending the stand off were suspended last week.
On Thursday evening, both Ecowas and the African Union expressed concern about the latest turn of events.
“We are always concerned when there is threat of a coup or reports on an ongoing ‘coup d'Etat’ in Africa. It is contrary to what we want the continent to be, that is a continent free of coups,” the African Union’s security commissioner Ramtane Lamamra said.