By Andrew Gray

ST PETERSBURG, Fla., Jan 16 (Reuters) - Pakistan's military is increasingly willing to fight Islamist militants and accept U.S. help with that mission, a top U.S. commander said on Wednesday.

Navy Adm. William Fallon, head of the U.S. military's Central Command, said tackling militants in the tribal areas of western Pakistan was also essential to stabilize neighboring Afghanistan.

Fallon said Pakistan's military had started to switch from its traditional focus on an external threat from eastern neighbor India to waging a counterinsurgency campaign against the internal threat from militants.

That shift had been driven by events of recent months, including the rise of militants in Pakistan's Swat Valley, the assassination of former Prime Minister Benazir Bhutto and the siege of the Red Mosque in Islamabad, Fallon said.

"They see they've got real problems internally, which are emanating from the west," Fallon told reporters in St. Petersburg, Florida, where he was hosting a meeting of military chiefs from the Gulf and Horn of Africa.

"My sense is there's an increased willingness to address these problems and we're going to try to help them," said Fallon, who is responsible for an area stretching from East Africa across the Middle East to central Asia.

Washington has given nuclear-armed Pakistan about $10 billion in aid since 2001, when Islamabad dropped support for the Taliban movement in Afghanistan and joined the U.S.-led campaign against terrorism after the Sept. 11 attacks on the United States.

CONCERNS ABOUT INSTABILITY

Fallon said be believed Pakistan's leaders now wanted a "more robust" effort by U.S. forces to train and advise their forces in counterinsurgency efforts.

The United States has already announced plans to step up training of Pakistan's Frontier Corps, a paramilitary force recruited from tribal areas.

Fallon did not give details of what other elements may be part of increased U.S. support for Pakistan's military.

But he said he was encouraged by conversations with Gen. Ashfaq Kayani, who took over as head of Pakistan's military from President Pervez Musharraf in November.

"I was very heartened by his understanding of what the problems are and what he's going to need to do to meet those, so we want to try and help that," said Fallon, who plans to visit Pakistan later this month.

U.S. officials have grown increasingly concerned about instability in western Pakistan, which they say has become a haven for Taliban and al Qaeda leaders.

Those leaders use the areas as a base to plan and launch attacks on Afghanistan, officials say.

"You can't ... think about Afghanistan without Pakistan because of the tremendous overlap, the border, the reality of the Pashtun tribal areas which encompass both countries," Fallon said.

He said cooperation along the border between U.S. forces in Afghanistan, Afghan troops and Pakistani forces had improved over the past year and he also detected better relations between Musharraf and Afghan President Hamid Karzai.

"In my personal discussions with both those leaders, I sense improvement as we've gone through the past year," Fallon said. "Hopefully that's going to continue." (Editing by John O'Callaghan)

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