By Manny Mogato and Raju Gopalakrishnan

MANILA, July 14 (Reuters) - Philippine President Gloria Macapagal Arroyo offered on Saturday to resume talks with communist rebels and said she would soon reach peace with Muslim militants despite a bloody battle earlier this week.

In an interview with Reuters in Manila's Malacanang Palace, Arroyo said she would devote her remaining three years in office to strengthening the economy, increasing the spread of education and ending the twin rebellions that beset the country.

The military has said the war with the communist New People's Army is the biggest security threat to the nation. Muslim rebels in the southern region of Mindanao, including the Moro Islamic Liberation Front (MILF), are seen as the next biggest threat.

"I would like to have peace in Mindanao and be able to crush the armed communists who terrorise people in pockets around the nation," Arroyo said.

But she said of the communists: "If they are still willing to to come to the table, we are still willing to come to the table. We would rather have peace than war."

Talks with the communists to end a 40-year rebellion have been stalled since August 2004. The government has offered to resume the talks before but the rebels rejected its demand for a ceasefire.

"We have to have some degree of confidence that there is sincerity on both sides to want to have peace," Arroyo said.

"With the MILF we can see the sincerity. We want peace and they want peace."

Arroyo, 60, said she was confident of reaching a peace deal with the MILF despite a battle between the military and MILF cadres on a southern island this week in which 18 people were killed, including 10 marines who were beheaded.

"They were victims of a decades-old battle that we can and will be able to end," she said.

ECONOMY

Arroyo came to power in 2001 when predecessor Joseph Estrada was ousted on charges of corruption following weeks of street protests. She won a single six-year term as president in 2004.

Although she was widely accused of cheating in that poll, most analysts accept that Arroyo has made determined efforts to improve the economy, including trimming the once runaway government deficit and some opening up of protected industries.

She increased taxes in 2006 and has vowed to attract foreign investment into mining, potentially one of the most lucrative sectors in the country.

"Already we have moved mountains with our macroeconomic reforms," Arroyo said.

"For the rest of the next three years, I want to transform the pain of the revenue-raising to the gain of having long-overdue investment in human and physical infrastructure that will bring investments and create jobs."

Government revenues have slipped this year, mainly due to endemic corruption in tax collection agencies and tax evasion, and Arroyo said that was next on her agenda.

"My vision for the nation is that in 20 years, we will be able to join the ranks of first world countries, where we have dramatically reduced poverty, created a robust middle class and have strong institutions," she said.

"I hope that by the time I leave office in 2010, we would have launched the country well on the way to achieving that vision.

"I hope that I will be remembered for having made tough decisions in order to effect permanent change in the economy."

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