Military leaders now in control of Burkina Faso must hand power to civilians or face consequences, the United Nations and African Union say.
UN West Africa envoy Mohamed Ibn Chambas said the military could face sanctions if they refused.
Meanwhile, thousands of people are gathering in the capital Ouagadougou to rally against the military takeover.
Days of protests forced President Blaise Compaore to step down on 31 October and flee to Ivory Coast.
Mr Compaore's attempt to extend his time in office was the immediate trigger for the protests.
But analysts say high prices, low wages and persistent poverty have fuelled wider discontent, particularly among younger Burkinabes.
Gunfire at state TV
The military takeover has infuriated opposition groups, who called a mass rally on Sunday against the army's "confiscation" of the uprising.
"The victory born from this popular uprising belongs to the people, and the task of managing the transition falls by right to the people," the groups said in a statement.
By early afternoon, thousands had turned out to protest in Ouagadougou's National Square, where one million had gathered earlier in the week to demand Mr Compaore's resignation.
On a makeshift stage in front of the crowd, one protester shouted into a microphone: "We are going to stay here. We are not going to move unless the military leave power."
Other protesters accused the military of being in league with Mr Compaore.
Elsewhere in Ouagadougou, witnesses reported hearing gunfire at the headquarters of state TV.
An unconfirmed report by the AFP news agency claimed that soldiers fired in the air to disperse protesters before seizing control of the building.
Meanwhile, the AU, UN, the US and regional economic bloc Ecowas all condemned the military takeover.
"We hope there will be a transition led by a civilian and in keeping with the constitutional order," Mr Chambas said.
"If not, the consequences are pretty clear. We want to avoid having to impose sanctions on Burkina Faso."
AU chief Nkosazana Dlamini-Zuma urged the military to "refrain from any acts or statements that may lead to further instability".
The US state department urged an immediate transfer of power to civilian authorities and a move towards free and fair presidential elections.
The army has quickly stepped in to fill the power vacuum, declaring Lt Col Isaac Zida the nation's transitional leader.
Col Zida was second-in-command of the presidential guard, and his selection apparently came after a power struggle with the overall army chief, Gen Honore Traore.
Under Burkina Faso's constitution, the president of the Senate should take over after the national president resigns and election should take place between 60 and 90 days afterwards.