According to the constitution the speaker of the House is supposed to take over, but there has been uncertainty as to who is in charge. The government announced on Tuesday that Nkurunziza, 55, had died of a heart attack although it was not clear which day he died.
Nkurunziza had been due to hand over power in August to President-elect Evariste Ndayishimiye, who successfully stood for the ruling party in elections last month.
The cabinet decided at an extraordinary cabinet meeting on Wednesday that the constitutional court should guide the country and “show modalities of filling the post,” the government statement said.
Burundi watchers have been keen to see whether the country’s powerful cabal of army generals and security chiefs who propped up Nkurunziza during his 15-year rule remain united over the succession.
Nkurunziza was a former rebel leader whose rule was marked by widespread brutality and repression against his opponents. The economy is also in tatters after donors, whose aid was a key source of government revenue, shunned it amid the human rights violations.
Authorities have not yet announced a date for Nkurunziza’s burial.
Nkurunziza became the president of the small, landlocked East African country in 2005.
He was re-elected in 2010 and in 2015 when he won a controversial third term despite opposition protests and international condemnation.
Nkurunziza's candidacy had been condemned as unconstitutional by the opposition, sparking months of protests and an attempted coup in May of that year.
His victory also triggered donor sanctions against the country.
But the government dismissed international criticism, including by the US, EU and former colonial power Belgium, which described the election as not credible.