African regional leaders have extended the mandate of Burundi's transitional president by four months and said elections must be held by 19 August.
President Ndayizeye was supposed to step down on Friday
President Domitien Ndayizeye's term of office was due to end on Friday, which, under a peace deal, should have coincided with elections.
The polls are supposed to end some 12 years of ethnic conflict.
On Thursday, former rebels now part of a power-sharing government, urged the leaders not to let Mr Ndayizeye stay.
They called him "an obstacle to peace".
"The transitional period is extended to 26 August, national elections will be held not later than 19 August and the swearing in will be on the 26th," Ugandan President Yoweri Museveni told reporters after the meeting of leader from east and central Africa.
"We have written to the mediators and to all the regional heads of state ahead of the Kampala summit, asking them not to extend Ndayizeye in his duties," the former rebel Forces for the Defence of Democracy (FDD) spokesman Karenga Ramadhani told AFP.
Correspondents say the call by the FDD has led to fears that the peace process may be in danger.
Rebel attacks continue
On Thursday, two people were killed in clashes between the army and the only active rebel group near the capital, Bujumbura.
The ethnic Hutu Forces for National Liberation (FNL) had offered to declare a ceasefire but army spokesman Adolphe Manirakiza said this was a "distraction", reports Reuters news agency.
Some 250,000 people have been killed in Burundi's 12-year civil war, which saw Hutu rebels fighting for a greater share of power from the Tutsi minority which has traditionally ruled the country.
Mr Ndayizeye is a Hutu but critics say he is a front for Tutsis who still wield the real power, through their domination of the military.
Former Hutu rebels are being integrated into the army.