WASHINGTON, Nov 18 (Reuters) - A Pakistani offensive against Islamists militants in the Bajaur region is pushing insurgents across the border into Afghanistan, where NATO forces have seen a rise in violence, a U.S. commander said on Tuesday.

Army Col. John Spiszer, who leads a NATO force of about 4,200 troops in four eastern Afghan provinces, said he expects violence to rise through the winter as militants take shelter from Pakistani forces in the mountainous border region.

"Unfortunately, or fortunately in some ways, the Pakistan military is doing operations that really ultimately are in some ways designed to drive (militants) out of Pakistan," Spiszer told Pentagon reporters via video link from a NATO base in Nangarhar province.

Violence levels against U.S. and NATO forces in Spiszer's area of operation, which also includes Kunar, Nuristan and Laghman provinces, increased last month as a result of military action by the Pakistani Army and Frontier Corps in the Federally Administered Tribal Areas, or FATA, he said.

That region of Afghanistan shares a remote and mountainous 250-mile (402-km) border with Pakistan's tribal areas that Western forces have not been able to secure.

U.S. officials have long said the Taliban, al Qaeda and other militant groups operate safe havens on Pakistan's side of the border that have been used to launch increasingly sophisticated attacks on U.S. and NATO forces in eastern Afghanistan.

Under pressure from Washington, Pakistan has mounted an offensive in the Bajaur region that lies to the east of Nangarhar and Nuristan provinces.

Spiszer said the Pakistani operations have been slow but sustained and effective at clearing militant bases.

"They're running out of options on places to go," he said. "We may see some increased violence trends over the winter that we haven't seen in the past. But if that is the case, it'd be because the Pakistan military's been taking away their safe havens in Pakistan."

Kunar province, currently the most violent eastern Afghanistan, saw the biggest single loss of life for U.S. forces last July when insurgents killed nine U.S. soldiers at a post in Wanat village.

Spiszer, who commands a brigade of the U.S. Army's 1st Infantry Division, said NATO and Afghan forces have stepped up border cooperation with the Pakistani military over the past month. Under an initiative called Operation Lionheart, which he said includes coordinated actions against militants on both sides of the border. (Reporting by David Morgan; Editing by Bill Trott)

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