"This decision is non negotiable," government spokesman Philippe Nzobonariba said in a radio broadcast, dismissing opposition demands the president step down.
The government said the electoral commission's proposal to delay the presidential election until July 15 was the final time polls would be postponed.
Around 40 people have died and scores more have been injured in protests that began when Nkurunziza announced in late April that he would stand again, after Burundi's constitutional court gave him the green light.
"They could tip an already extremely tense situation over the edge," Zeid Ra'ad Al Hussein said in a statement.
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"The last thing Burundi needs after a decade of gradual and largely successful peace-building is to be catapulted back into civil war because of a small number of people's ruthless determination to retain, or gain, power at any cost," he added.
Nearly 100,000 Burundians have sought refuge in neighbouring countries.
But Nzobonariba said the "vast majority" had "fled because of the terrorist rumours spread by politicians who do not want elections, aided by some foreigners and some non-governmental organisations who want to push Burundi into chaos."
The president survived a coup attempt last month and has since faced down international pressure, including aid cuts, aimed at forcing him to reconsider.
The opposition has rejected proposals for the new election timetable, saying conditions for holding fair polls were not met.
"If things remain as they are, we consider that it will be a masquerade, a parody of elections," opposition leader Charles Nditije told AFP late yesterday, demanding the setting up of a new independent electoral commission.