There has been widespread condemnation of Mali's troops, after they ousted President Amadou Toumani Toure.
The UN Security Council called for the "immediate restoration of constitutional rule and the democratically elected government".
The World Bank and African Development Bank said they were suspending all aid until the crisis is resolved.
The coup leaders went on state TV to say they had closed the borders. They added that the president was safe.
A government official told the BBC that President Amadou Toumani Toure was not in the custody of mutineers.
Meanwhile, soldiers looted the presidential palace in the capital Bamako, following the coup.
In a separate development, Kenya's Foreign Minister Moses Wetangula and his delegation are stranded in the country, as Bamako's airport is closed.
They were attending an African Union meeting on peace and security.
The West African regional body Ecowas said the mutinous soldiers' behaviour was "reprehensible".
The African Union described the coup as a "significant setback for Mali".
France, the former colonial power, also suspended its aid in protest.
The soldiers, calling themselves the Committee for the Re-establishment of Democracy and the Restoration of the State (CNRDR), have promised to hand over power to an elected government.
They said they had led Wednesday's mutiny because the government had not giving them enough arms to tackle a rebellion by ethnic Tuareg in the north of Mali.
They attacked the presidential palace, traded gunfire with soldiers loyal to the government and took over the state radio and TV broadcaster in Bamako and took it off air.
The leader of the mutiny is Capt Amadou Sanogo. In a brief TV appearance on Thursday, he announce the imposition of a national curfew and said the constitution had been suspended.
The BBC's Martin Vogl in Bamako says it is possible that the coup may falter, pointing out that the mutinous troops are poorly equipped, led by a mid-ranking soldier and they do not have the backing of all Malian forces.
The well-trained and organised Red Berets unit is loyal to the president and he is believed to be under their protection, our reporter says.
A source told the BBC that the foreign minister and a number of other ministers had been arrested by the renegade soldiers.
Mali has had democratic rule for the last 20 years, during which it has come to be considered as a model which other emerging democracies can look to.
The unrest began on Wednesday as the country's defence minister started a tour of military barracks north of the capital.
Soldiers upset with the government's handling of the Tuareg rebellion fired in the air during the inspection, prompting an immediate strengthening of security around the presidential palace.
The Tuaregs have forced the army out of several northern towns in recent months.
A presidential election was due to take place in the country in just under a month.
The government had so far refused to postpone the poll, despite the unrest involving Tuareg-led rebels.
Both the US and France have urged the soldiers and government to resolve their dispute through peaceful means.