Officials of the Regional Peace Initiative for Burundi, led by South African safety and security minister Charles Nqakula, were in Bujumbura, the capital, to urge the two parties to speed up the process ahead of a 31 December deadline.
"The mandate [of the mediation process] will not be reviewed; everything that needs to be done has to be done before 31 December; this includes the assembly of FNL combatants in the designated areas so that we can begin the disarmament, demobilisation and reintegration [DDR]; essentially, that is the message we came to convey to the two parties," Nqakula said.
Nqakula, who was accompanied by Uganda's Foreign Minister Sam Kutesa, presented a new plan to revive the stalled peace process to President Pierre Nkurunziza and FNL leader Agathon Rwasa.
However, the FNL immediately rejected a proposal requiring it to drop "Palipehutu", which means "for the Hutu alone", from its name.
Its use in FNL's official name and the registration of the group as a political party led to a stalemate in the talks between the government and the country's remaining rebel group.
"We will not change our name, we signed the [peace] accords as the PALIPEHUTU-FNL, they should accept us as such," Pasteur Habimana, FNL spokesman, said.
By proposing the change of name, Habimana said, the mediator had surrendered his responsibility as the guarantor of the peace accords signed in 2006 between the government and FNL.
Saying that the peace process had taken too long and should be concluded, Nqakula stressed: "There is nothing that has no end, we must come to the end of the road in terms of ensuring that all the building blocks for durable peace in Burundi are in place."
At a press conference on 6 November, Nkurunziza's spokesman, Léonidas Hatungimana, said the government was satisfied with the regional initiative's formula to get the peace process back on track.
The regional initiative recommends that the government integrate FNL members into its institutions, in accordance with the constitution.
"A list of places available for PALIPEHUTU-FNL is ready and has been communicated to Agathon Rwasa," Hatungimana said.
However, FNL rejected the offer, saying it was not up to the government to propose posts. "The government proposes [to give] us just scraps; we should sit together and negotiate," Habimana told reporters.
According to Burundi's constitution, FNL will only get posts that do not require elections, such as provincial governors or posts in public administrations. It cannot get seats in the National Assembly or Senate.
FNL said it was ready to have its combatants in assembly areas, but criticised the poor living conditions at the assembly points.
So far, only 2,000 FNL combatants are assembled at Rugazi in the northwest province of Bubanza. The FNL claims it has at least 21,000 combatants waiting to join assembly areas.
The head of the government's delegates to the joint Verification and Monitoring Mechanism, Brig-Gen Lazare Nduwayo, said preparation for another cantonment site in Bubanza province to host about 8,000 FNL combatants had been delayed but the site would be ready soon.