West Africa's main regional and economic bloc ECOWAS called on the plotters to free Bazoum. The African Union urged the "felon" soldiers involved to return to barracks immediately.
The president of neighboring Benin, Patrice Talon, said he was going to Niger on Wednesday to mediate after meeting with Nigeria's president and ECOWAS leader Bola Tinubu.
"I believe that all means will be used, if necessary, to restore constitutional order in Niger, but the ideal would be for everything to be done in peace and harmony," Talon told reporters in Abuja.
The national army was ready to attack the guards if they did not come to their senses, Niger's presidency said in a statement.
That statement followed reports that presidential guards had cut access to the palace and blocked Bazoum inside, raising concern West Africa's seventh coup since 2020 could be under way.
"The President of the Republic and his family are well," the presidency said on social media at 12:30 local time (1130 GMT) without providing further details.
Another post which said the presidential guards had started a movement "in vain" was later deleted amid doubts about who was in control. Soldiers had taken control of all roads leading to the national television station.
An adviser to the presidency, speaking on condition of anonymity, told Reuters around 1400 GMT that negotiations were under way between Bazoum's camp and the leaders of the presidential guard. Reuters was unable to corroborate this information.
The rest of Niamey appeared calm, with normal traffic on the road and full internet access, a Reuters reporter said.
A military takeover in the former French colony could further complicate Western efforts to help countries in the Sahel region fight a jihadist insurgency that has spread from Mali over the past decade.
Land-locked Niger has become a pivotal ally for Western powers seeking to help fight the insurgency but facing growing acrimony from the new juntas in charge in Mali and Burkina Faso. It is also a key ally of the EU in the fight against irregular migration from sub-Saharan Africa.
"The EU condemns any attempt to destabilize democracy and threaten the stability of Niger," EU foreign policy chief Josep Borrell said in a post.
France also condemned any attempt to seize power and advised French citizens in Niamey to act with vigilance. The United States said it was deeply concerned by developments.
United Nations Secretary-General Antonio Guterres called on all actors to exercise restraint, his office said in a statement.