The condemnation came as security forces cracked down on protests against Nkurunziza in and around the capital Bujumbura on Tuesday.
"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.
"The Burundian government will not negotiate and will not discuss matters that undermine our institutions," he added.
Al Jazeera's Haru Mutasa, reporting from a protest site in Bujumbura on Tuesday, said that police appeared to have fired live rounds, in addition to tear gas, to disperse demonstrators who were trying to march in the centre of the city.
She also said that demonstrators used cars to form a barricade in the street, in a bid to protect themselves from being shot at by security forces.
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.
Nkurunziza, a former rebel leader, argues that his first term did not count as he was elected by parliament, not directly by the people.