However, Prime Minister Isaac Zida, who was also detained when the presidential guard stormed a cabinet meeting on Wednesday, remains under house arrest.
The African Union has suspended Burkina Faso and threatened sanctions unless the junta releases all interim political figures from detention.
The US and France have also condemned the coup in the former French colony.
The coup leaders have agreed to the “principle of dialogue”, as two West African leaders arrived in the country to mediate in the crisis.
At least three people have died in protests in the capital, Ouagadougou, after an ally of ex-President Blaise Compaore was named leader on Thursday.
The influential Balai Citoyen civil society group has put the number of people who have died in demonstrations against the presidential guard (RSP) , at 10.
An unknown number of protesters have also been detained.
The BBC’s Laeila Adjovi in Ouagadougou says demonstrators gathered around the airport for the arrival of a delegation from the regional body, the Economic Community of West African States (Ecowas).
The delegation was led by Senegal’s President Macky Sall, the current Ecowas chair, and Benin’s leader Thomas Boni Yayi.
Ahead of their arrival, the air and land borders were officially re-opened.
Security forces again fired in the air on Friday to disperse to demonstrators who burned tyres and blocked streets in the city, our reporter says.
Elections were due to be held in the West African nation on 11 October, nearly a year after a popular uprising forced Mr Compaore, the long-time ruler of the West African country, from power.
Coup leader Gen Gilbert Diendere, who was Mr Compaore’s former chief-of-staff, told reporters that Mr Kafando was now in his official residence.
He was reportedly freed on Thursday but has not yet been seen in public.
Two other minister have also been released, the coup leaders say.
The decision to free them was made “as a sign of easing tensions and in the general interest”, a statement read on national television said.
Prime Minister Zida was the army officer who took charge after Mr Compaore was ousted.
The lieutenant colonel was number two in the RSP, where he may still hold influence, which explains his continued detention, says BBC Afrique’s Lamine Konkobo.
Mr Compaore is currently in exile and was accused of committing widespread abuses, and trying to change the constitution to extend his term in office.
Some of his key allies had been barred from contesting the election.
Gen Diendere has said he has had no contact with Mr Compaore and will do everything to “avoid violence that could plunge the country into chaos”.
An earlier announcement on state television said wide-ranging talks would be held to form a new interim government that would organise “peaceful and inclusive elections”.
Transitional parliamentary speaker Cheriff Sy called for people to “immediately rise up” against the coup, and declared himself the leader.
The coup was announced on the day that a judge was due to give the results of DNA tests on the remains of former President Thomas Sankara, his widow Mariam Sankara told the BBC.
Her husband was killed in a 1987 coup that saw Mr Compaore and fellow officers such as his close friend Gen Diendere take power.
The family want to know the exact circumstances of his death, which have always been shrouded in mystery.