The warning comes after Ntamwana accused the rebels of murdering the Vatican's ambassador to Burundi, Michael Courtney.
"We are very serious and clear on this: he has 30 days to leave Burundi, not one day more," FNL spokesman Pasteur Habimana said.
"We ask the Catholic Church in Rome to find another host country for Simon Ntamwana in the coming days," he added.
"We swear solemnly to the people of Burundi and the Church that we did not organise the ambush against the Vatican ambassador," Habimana said.
Courtney was killed in an ambush on Monday, and Ntamwana said the rebels were responsible, describing the attack as "a real execution."
The FNL has said the army was responsible for Courtney's death, which was unprecedented in the Vatican's modern-day history. During the 20th century, no Vatican ambassadors were killed despite the Roman Catholic Church going through some of its most troubled periods, such as World War II and the Cold War.
Some 1,500 people attended the funeral service for Courtney in Bujumbura, before his body was flown back to Ireland for burial.
"We swear solemnly to the people of Burundi and the Church that we did not organise the ambush against the Vatican ambassador"
National Liberation Forces (FNL) spokesman
The FNL is the only armed Hutu group still active in Burundi, where civil war has claimed more than 300,000 lives since 1993.
All other Hutu rebel groups have made peace with the government and even joined its ranks, but the FNL refuses to recognise the administration's legitimacy.
Courtney had been instrumental in convincing these other groups to give up their armed struggle and had made numerous appeals to the FNL to follow suit.