They said the management of the transition belonged to the people and should not be confiscated by the army.
The move came hours after the army said Lt-Col Isaac Zida, second-in-command of the presidential guard, had been chosen as the nation’s transitional leader.
Blaise Compaore has fled to Ivory Coast.
“The victory born from this popular uprising belongs to the people, and the task of managing the transition falls by right to the people,” opposition groups said in a statement.
“In no case can it be confiscated by the army.”
There were protests earlier this week after Blaise Compaore sought to amend the constitution and extend his long hold on the presidency.
On October 30, protesters set fire to parliament and government buildings in the capital Ouagadougou.
Under Burkina Faso’s new constitution, the president of the Senate should take over after the national president resigns, with elections taking place between 60 and 90 days afterwards.
The African Union (AU) has called for a “civilian-led transition” culminating as soon as possible in “the holding of free, fair and transparent elections”.
In a statement, 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 in Burkina Faso and a move towards free and fair presidential elections.
The unveiling of Lt-Col. Nkosazana Dlamini-Zuma as interim leader came after what analysts say was a 24-hour power struggle within the army.
The army statement’s was signed by army chief General Honore Traore, who had declared himself head of state in the immediate aftermath of President Blaise Compaore’s resignation.
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