But with several protest leaders having left the country and others in hiding, it is unclear whether many opposition members will actually heed the call to march.
Protests against Nkurunziza's decision to run for a third term have been going on for weeks. More than 20 people have been killed by security forces and 90,000 people have fled to neighbouring countries.
The call for fresh protests came as Burundi's government on Monday held out the possibility of a postponement of elections.
Parliamentary elections are currently scheduled to take place on June 5 while the presidential election is slated for June 26.
A summit of leaders of the East African Community - comprising Rwanda, Kenya, Tanzania and Uganda - and South Africa's President Jacob Zuma on Sunday called for postponement of the elections for at least a month and a half.
Presidential spokesman Gervais Abayeho said the electoral commission was looking into the request and would advise the government.
"They will make a proposal to the government to see if it is possible to make some adjustments on the calendar. But the government is receptive of the proposal made by the summit," he said.
"We believe any reshuffle of the calendar will be anytime soon. I think there will be some slight reshuffle."
The opposition and rights groups say the president's third-term bid violates a constitutional two-term limit as well as a 2006 peace deal that ended a 13-year civil war, Al Jazeera reported.