It is believed President Tandja is being held at a military barracks in Niamey
The African Union has suspended Niger following Thursday's military coup, in which President Mamadou Tandja was deposed and the government dissolved.
The organisation said it had imposed sanctions on the country and demanded a return to constitutional rule.
UN Secretary General Ban Ki-moon also condemned the coup, and appealed for calm and respect for human rights.
Earlier, the new military council announced it was lifting a curfew and re-opening borders.
Col Abdul Karimou said the situation was "under control" and that there was "no single voice of dissension" in the West African state.
Thousands of people took to the streets on Friday in support of the takeover.
Ten people are said to have died when the junta seized power.
Troops stormed the palace during a cabinet meeting on Thursday afternoon, seizing Mr Tandja and his ministers before announcing that they were suspending the constitution and dissolving all state institutions.
Col Goukoye Abdul Karimou read a statement signed by Col Salou Djibo
Calling themselves the Supreme Council for the Restoration of Democracy (CSRD), the coup leaders promised to turn Niger into an example of "democracy and good governance" and save its people from "poverty, deception and corruption".
A senior army officer, Col Salou Djibo, was named head of a military government.
The US said it believed the coup had been triggered by Mr Tandja's actions last August, when he held a controversial referendum to abolish limits on presidential terms of office.
The opposition Co-ordination of Democratic Forces for the Republic (CFDR) - a coalition of political parties, trade unions and human rights groups formed last year to protest against the constitutional changes - welcomed it.
Chronic poverty Population 14 million, 61% live on less than $1 a day
Resource rich Huge reserves of uranium, Chinese firms digging for oil
Politically unstable History of coups, assassinations and on-off rebellion by nomadic Tuareg people in the north
In a statement, the group condemned "President Tanja's stubbornness in power", and called on the junta to respect its pledge to restore democracy.
Mr Tandja, a 71-year-old former army officer, was first elected in 1999 and was returned to power in an election in 2004.
His second term in office expired in December, but was extended to allow him to complete major investment projects.
A junta spokesman, Col Goukoye Abdul Karimou, told the BBC on Friday that the president was "safe and well".
"We are taking care of him - remember he is one of our elder soldiers," he told the BBC's Focus on Africa.
The colonel said most of the cabinet ministers captured along with the president had been released and had gone home.
The three still being held would be free in a couple of days, he added.
It is believed they are being held at a military barracks in Niamey.
The international community has been quick to condemn the coup.
Niger is suspended from all activities of the AU. Meanwhile, we will continue with the process of helping them return to constitutional order
Mull Sebujja Katende, African Union Peace and Security Council
The European Union followed former colonial power France in calling for all those involved to "engage immediately in a democratic process allowing for rapid establishment of the constitutional order".
The chairman of the African Union Commission, Jean Ping, said there should be "zero tolerance" of those taking power by force.
The regional organisation later announced that it had suspended Niger and called for its citizens to be allowed to elect the leader they wanted.
"Niger is suspended from all activities of the AU. Meanwhile, we will continue with the process of helping them return to constitutional order," said Mull Sebujja Katende, the chairman of the AU Peace and Security Council.
In New York, the UN's secretary general reiterated "his disapproval of unconstitutional changes of government as well as attempts to remain in power through unconstitutional means".
Mr Ban noted the CSRD had said it intended to restore constitutional rule and called on it "to proceed swiftly with these efforts through a process that is consensual and that includes all segments of Nigerien society".
Niger has experienced long periods of military rule since independence from France in 1960.
It is one of the world's poorest countries, but Mr Tandja's supporters argue that his decade in power has brought a measure of economic stability.
Under his tenure, the French energy firm Areva has begun work on the world's second-biggest uranium mine - ploughing an estimated $1.5bn (£970m) into the project.
China National Petroleum Corporation signed a $5bn deal in 2008 to pump oil within three years.
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