(Adds new President comments, details)

By Brian Benza

GABORONE, Nov 1 (Reuters) - Botswana's new president Duma Boko said on Friday he wanted to conclude talks for a new sales pact with global diamonds mining giant De Beers as soon as possible.

"The relationship with De Beers could have been damaged by the way the negotiations were handled," President Boko said in a televised statement from Gaborone, Botswana's capital. "The first thing that needs to be done is to engage the other party".

De Beers, a unit of Anglo American , last year agreed a new diamond sales pact, which will see the government's share of diamonds from the Debswana joint venture gradually increase to 50% over the next decade.

Debswana Diamond Company, equally owned by Botswana and De Beers, currently sells 75% of its output to De Beers.

While the Botswana government and the outgoing president Mokgweetsi Masisi touted the merits of the deal, it has yet to be signed. Boko said De Beers had been "considering walking away, not signing at all ... (a) very dangerous position to be in as a country."

Boko said that his new administration wants to engage with De Beers to understand its concerns.

"A proper negotiation involves compromise, where you get a bit of what you wanted, the other person gets a bit," Boko said. "Then...you have a durable, sustainable agreement."

Anglo is working on a plan to divest De Beers as part of a broader restructuring of its sprawling business. Masisi in July had said the Botswana government may raise its shareholding in De Beers from its current 15%.

Like other luxury goods, diamond prices have been hammered by a slump in global demand. De Beers has been limiting supply and offering flexibility to contracted customers.

(Reporting by Brian Benza in Gaborone, additional reporting by Felix Njini in Johannesburg, Clara Denina in London Editing by Mark Potter and Ros Russell)

((Felix.Njini@ThomsonReuters.com; Reuters Messaging: Felix.Njini@ThomsonReuters.com))