Burundi's government on Tuesday condemned mounting diplomatic pressure over President Pierre Nkurunziza's controversial bid to stand for a third consecutive term, signalling it would not bow to international criticism.

"The government of Burundi is profoundly preoccupied by the current diplomatic activity which could undermine and denigrate our republican institutions and constitution," government spokesman Philippe Nzobonariba said on state radio.

He said the Burundian government had "red lines", indicating that Nkurunziza was still unwilling to compromise even though the political crisis has already sparked weeks of civil unrest, an attempted coup, a refugee crisis and international isolation.

"Certain questions that touch on our sovereignty, constitution and the primacy of our laws cannot be debated," Nzobonariba said.

"The Burundian government will not negotiate and will not discuss matters that undermine our institutions," he added.

Burundi's crisis, which began after the ruling party nominated Nkurunziza to stand again in the June 26 presidential election, deepened earlier this month when a top general staged a failed coup attempt.

Parliamentary polls, initially set to take place on Tuesday, have been postponed to June 5.

Opposition and rights groups say that Nkurunziza's bid for a third five-year term violates the constitution as well as the terms of a peace deal that ended a 13-year civil war in 2006.

That conflict, marked by brutal ethnic violence between the country's ethnic Hutu and Tutsi communities, left hundreds of thousands dead, and there are fears the latest unrest could plunge the small, landlocked and impoverished nation back into widespread violence.

Nkurunziza, a former rebel leader and born-again Christian, argues that his first term did not count as he was elected by parliament, not directly by the people.

He has so far resisted the protests and international pressure and intends to maintain his bid for another term, for which he has strong support in rural areas and among sections of the Hutu majority.