(Adds background, Museveni)

By Patrick Nduwimana

BUJUMBURA, Dec 4 (Reuters) - Burundi's government and last remaining rebel group committed on Thursday to implement a peace agreement that had been delayed by a dispute over the insurgents' transformation into a political party.

At a summit of regional leaders, President Pierre Nkurunziza and Forces for National Liberation (FNL) leader Agathon Rwasa signed a communique saying disarmament and demobilisation of rebels would start "without delay".

The pair smiled and shook hands after signing.

The FNL, whose fighters hold the hills outside the capital Bujumbura, had dropped its demand to form a political party called "Palipehutu", which means party for the liberation of Hutus, the communique said.

Burundi's constitution does not allow parties with ethnic affiliations.

Increasingly impatient mediators, led by South Africa, had given the government and rebels until the end of this year to complete agreement or risk losing regional support.

The government and FNL first reached a deal in principle in mid-2006 to halt two decades of violence that killed 300,000 people in the central African nation of 8 million.

Thursday's communique said senior FNL members would take 33 government posts, and the government would release all political prisonsers and prisoners of war.

"Both parties agree that the disarmament, demobilisation and reintegration process is to begin without delay with FNL combatants moving into assembly areas as soon as possible," the communique added.

"The Palipehutu FNL recognises that the name of the party as it currently stands cannot be registered as a political party as it is not permissible within the constitution of Burundi."

The FNL is to find a new name by Dec. 31, it added.

Regional leaders applauded at the signing.

"I take this opportunity to salute and congratulate President Nkurunziza and Agathon Rwasa for signing this communique, which is going to normalise the conclusion of the peace process," Ugandan President Yoweri Museveni said.

"We are sure that we are coming to the end of this sad history in Burundi."

(Writing by Andrew Cawthorne; editing by Michael Roddy)

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