The United Nations has joined global condemnation of the military takeover in Mali, which saw President Ibrahim Boubacar Keïta forced to resign.
The UN's Security Council echoed similar calls by regional bodies for the immediate release of all government officials and the restoration of constitutional order.
The soldiers said they acted to prevent the country falling into further chaos.
They say they will set up a civilian government and hold new elections.
Mali, a vast country stretching into the Sahara Desert, is among the poorest in the world and has experienced several military takeovers. It is currently battling to contain a wave of jihadist attacks and ethnic violence.
Mr Keïta won a second term in elections in 2018, but since June has faced huge street protests over corruption, mismanagement of the economy and disputed legislative elections.
There has also been anger among troops about pay and the conflict with jihadists.
The African Union earlier suspended Mali, saying military coups were "something of the past which we cannot accept anymore".
"Whenever you have a crisis and the military people have a coup and say 'we are responding to the will of the people', this way of responding is not acceptable at all," the AU's Commissioner for Peace and Security, Smail Chergui, told the BBC's Focus on Africa programme.
The 15-member Economic Community of West African States (Ecowas) has also taken swift action against Mali - closing borders, suspending financial flows and ejecting it from decision-making bodies. It is currently holding a virtual conference to decide what further action to take.
US Secretary of State Mike Pompeo tweeted his condemnation.
The U.S. strongly condemns the August 18 mutiny in Mali. We join our international partners including the Economic Community of West African States and the @_AfricanUnion in denouncing these actions.— Secretary Pompeo (@SecPompeo) August 19, 2020
French President Emmanuel Macron also urged a return to civilian rule, saying "the fight against terrorist groups and the defence of democracy and the rule of law are inseparable".
France, Mali's former colonial ruler, has several thousand troops based in Mali fighting Islamist militant groups and its Armed Forces Minister Florence Parly tweeted that this operation would continue.
Various jihadist groups, some linked to al-Qaeda and the Islamic State group, are based in the deserts of northern Mali, from where they have spread to neighbouring countries, especially Burkina Faso and Niger.
Who are the coup leaders?
Colonel Assimi Goita has presented himself as leader of the new military junta, which is calling itself the National Committee for the Salvation of the People (CNSP) but little is known about him.
Col Goita, said to be the head of Mali's special forces, met senior civil servants earlier on Wednesday and told them: "We have no political ambitions, we are soldiers, our objective is to rapidly transfer power. The state will continue, we assure you of our support in order to work in tranquillity, we want to reassure you," the Malian newspaper Journal du Mali reports.
Other members of the junta identified in the report include Col Malick Diaw, CNSP vice-president, and Col Ismaël Wagué, the air force deputy chief of staff, who had earlier read a statement on behalf of the group.
The newspaper quotes local websites as saying four civilians were killed by gunfire during the military takeover, although this has been denied by coup leaders.
What does the opposition say?
One of the parties in the M5 opposition coalition, CMAS, said it would support the coup leader in "developing a roadmap" towards new elections and called for rallies on Friday "to celebrate the Malian people's victory".
After meeting the coup leaders, the head of Mali's opposition M5 movement, conservative Imam Mahmoud Dicko, announced he would be withdrawing from politics. No reasons were given.
Mr Dicko was one of the key figures in the huge street protests calling for Mr Keïta to resign.
How did the coup take place?
It appears that mutinying soldiers took control of the Kati army camp, about 15km (nine miles) from Bamako, on Tuesday. They then marched on the capital, cheered by crowds who had gathered to demand Mr Keïta's resignation.
The soldiers then stormed the presidential buildings, arresting Mr Keïta and his prime minister and taking them to Kati Camp. The president's son, the speaker of the National Assembly, the foreign and finance ministers were also reported to have been detained.
Appearing on TV on Tuesday night, President Keïta said he would resign as he did not want "blood to be spilled to keep me in power".
Although banks and offices were closed in Bamako on Wednesday, there were signs of daily life resuming. Some residents had gathered to celebrate the coup, while some were worried about who would now be in charge of the country, reports journalist Mohamed Salaha.
It was the war in Libya, almost a decade ago, that nudged Mali along the path to chaos.
Weapons from Libya flooded across the Sahara Desert, fuelling a separatist conflict in northern Mali, which morphed into an Islamist militant offensive, which prompted a coup in the capital Bamako.
It's been a mess ever since, in a landlocked nation that had been a West African success story.
Today French troops, American drones, UN peacekeepers, and British helicopters are all trying - and largely failing - to strengthen security, not just in Mali, but across a vast region increasingly threatened by Islamist insurgencies and other conflicts.
This latest military coup in Bamako appears to be a reaction to those security challenges, but also to corruption, disputed elections, and political drift.
The coup itself seems unlikely to fix anything.
But it highlights a familiar truth - that while foreign intervention has its uses, the key to repairing a nation like Mali lies in its own hands, and with its own faltering democratic institutions.