(Adds detail and quote from PM in pars 2-3, Rio Tinto response...

(Adds detail and quote from PM in pars 2-3, Rio Tinto response in pars 6-7)

ULAANBAATAR, Dec 13 (Reuters) - Anglo-Australian mining giant Rio Tinto (RIO) RIO.L has agreed to write off Mongolia's outstanding $2.3 billion debt for its share in the massive Oyu Tolgoi copper-gold project, Prime Minister Oyun-Erdene Luvsannamsrai said on Monday.

Oyun-Erdene said his office had received a letter from Rio Tinto agreeing to write off the debt, conduct an independent audit into the financing of the project's underground expansion and improve governance.

"We have proposed that the benefits of Oyu Tolgoi be in the interests of the Mongolian people," Oyun-Erdene told a briefing.

He said Rio also agreed the much-delayed expanded underground section of the mine would be completed by 2023.

Oyu Tolgoi is Mongolia's biggest investment project but it has been subject to frequent disputes and delays, with Mongolian politicians repeatedly calling for the original investment agreement to be redrawn.

A Rio Tinto spokesman said in a statement the offer made to Mongolia "aims to reset the relationship and allow all parties to move forward together", without providing details of the debt writedown offer.

"The offer reflects months of discussion between Rio Tinto, TRQ (subsidiary Turquoise Hill Resources TRQ.TO ) and the Government of Mongolia to understand the Government's issues and priorities, deliver greater economic value to Mongolia and build a stronger partnership for a prosperous future for all.”