Zedi Feruzi, the leader of the UPD party, was killed along with his bodyguard in a drive-by shooting in Bujumbura, Pierre Nkurikiye said.
President Pierre Nkurunziza's office said that it was "very moved by the assassination."
The killers have not yet been identified, Nkurunziza's office said in a statement. A radio journalist was seriously wounded in the attack near Feruzi's home.
The violence comes a day after at least three people were killed and 21 were wounded by two grenades thrown in a market attack in Bujumbura. A suspect is in custody, Nkurikiye told CNN earlier.
The turmoil, much of it centered around Nkurunziza's decision to seek a third term, has been ongoing for more than a month. Such a re-election bid is prohibited by the agreement that ended the nation's 1993-2003 civil war, yet the President is pushing forward nonetheless.
Earlier this week, he moved the elections to June 6, 10 days later than originally scheduled.
Protesters determined to prevent his candidacy have demonstrated in the capital and police have met them with deadly force. Such clashes haven't let up, with the almost daily protests continuing on Saturday. More than 20 people have been killed in the demonstrations, including at least five policemen, Burundian government spokesman Willy Nyamtiwe said.
The military has sometimes acted as a buffer between police and protesters. That happened again Wednesday in Bujumbura, with troops urging police not to fire live rounds on protesters.
More than 110,000 people have fled to Tanzania and other neighboring countries, U.N. spokesman Farhan Haq said Thursday. At least 27 of them have died of cholera they contracted in refugee camps.
The United States has said that "the decision by the Burundian President Nkurunziza to disregard the Arusha Agreement to run for a third term has created instability and violence."