In a statement, the military unit also announced the closure of the West African nation's borders as well as the implementation of an overnight curfew.
Coup spokesperson Lieutenant-Colonel Mamadou Bamba spoke on national television to announce that "wide-ranging talks" were being held to form a new government leading to "inclusive and peaceful elections".
He added that the coup had put an end to “the deviant regime of transition” in the West African state.
Presidential guard members linked to ex-leader Blaise Compaoré had burst into a cabinet meeting on Wednesday and seized acting President Michel Kafando, Prime Minister Isaac Zida and two ministers.
Zida was himself once an officer in Compaore's powerful Presidential Security Regiment (RSP), before he toppled his boss after days of street protests in October 2014.
Shots could still be heard Thursday in the capital Ouagadougou after the arrest of the nation's transitional leaders triggered immediate street protests outside the presidential palace where they were reportedly being held.
Revolution Square – the epicentre of protests against Compaore – was empty apart from military patrols, with the streets of the capital also deserted.
Interim parliament speaker Moumina Cheriff Sy denounced what he said was a "coup d'Etat", and in an interview with Radio France Internationale (RFI) radio Thursday called on the people to "immediately rise up".
Sy called the detention of the president and prime minister "a serious attack on the republic".
International condemnation was swift, with the United Nations Security Council and the European Union, one of the main donors to the poverty-stricken country, demanding the immediate release of the country's transitional leaders, and UN Secretary-General Ban Ki-moon expressing his outrage.
President Francois Hollande of France – the former colonial power – joined the chorus of disapproval, calling for political order "to be restored".
In a joint statement, the United Nations, the African Union and the Economic Community of West African States (ECOWAS) demanded "the immediate and unconditional release of the hostages".
Protesters marching on the presidential palace on Wednesday evening were met with bursts of gunfire, with shooting also heard around the complex Thursday.
Crowds of several hundred shouting "Down with the RSP" gathered with whistles and vuvuzelas near the palace after news spread, with the headquarters of Compaore's Congress for Democracy and Progress (CDP) party ransacked.
Troops threaten to kill radio staff
Broadcasts by Radio France Internationale (FRANCE 24’s sister station) and the private Omega radio station were cut.
Omega boss Alpha Barry told FRANCE 24 television that RSP troops had threatened to kill staff if they did not stop transmitting.
The country's main trade unions launched a joint appeal "to observe a general strike throughout the national territory (...) against the RSP interference in politics and for a true democracy".
While the RSP's demands were not yet known, it has repeatedly tried to disrupt the ongoing transition.
On Monday the country's National Reconciliation and Reforms Commission had recommended that the 1,300-man force, considered the landlocked country's best troops, be disbanded.
A transitional government had been in place since ex-president Compaore fled into exile following violent protests in 2014, and was charged with running the nation until presidential and legislative elections could be held on October 11.
Supporters of Compaore were banned from standing in the upcoming elections under a controversial election law passed in April, which made anyone who supported "unconstitutional change" ineligible to run.
On the ground, the Balai Citoyen ("Civic Broom") movement, which was at the forefront of last year's anti-Compaore protests, called for protesters to gather to "say no to the coup d'Etat under way", an appeal that was shared widely on social networks.
State television was broadcasting its usual cartoons and a football match. Its buildings have traditionally been guarded by the RSP.