By Chris Allbritton

ISLAMABAD (Reuters) - After years of demanding Pakistan crack down on militants in a lawless tribal area on its border with Afghanistan, the United States has now set out a possibly tougher challenge -- bring those militants to the peace table.

It's a tough task. Ties have been strained between the two allies for months since Osama bin Laden was found holed up in a town two hours from Islamabad.

And there are doubts the Pakistanis can, or will, persuade the al Qaeda-linked Haqqani network to take part in the nascent peace process to end the Afghan war, given Pakistan's ties to the militants and its competing interests in the region.

On a two-day visit to Islamabad last week, U.S. Secretary of State Hillary Clinton called Pakistan's relationship with the Haqqanis akin to keeping "snakes in your backyard".

She demanded that Pakistan deny the group any safe haven in the border zone. The network is one of the most effective factions of the Afghan Taliban-led insurgency and was blamed for an attack on the U.S. Embassy in Kabul last month,

But talking with militant groups has been a long-standing effort by the United States as it prepares to withdraw troops from Afghanistan, and Clinton herself said there had been U.S. overtures to the Haqqanis. Now she wants Pakistan's help.

"We think that Pakistan, for a variety of reasons, has the capacity to encourage, to push, to squeeze ... terrorists, including the Haqqanis and the Afghan Taliban, to be willing to engage on the peace process," she said during her visit.

Clinton's comments seemed to be well-received by a Pakistan public weary of war and increasingly convinced the U.S.-led global fight against militancy is not its battle.

Pakistan says it has sacrificed more than any other country and says up to 40,000 civilians, troops and security personnel have been killed since 2001.

But it also reflects the reality that the United States is running out of options in Afghanistan.

"They have recognized the principle of talking to the Taliban. It's almost a natural thing to talk to the others," said Ayesha Siddiqa, a noted defense analyst. "And secondly, what are the options?"

BOLD ATTACKS

Across Afghanistan, U.S. and NATO forces have been unable to deal a decisive blow to Taliban insurgents and their allies like the Haqqanis, blamed for a series of bold attacks on American targets. More than 2,700 NATO troops have been killed since 2001, as well as more than 11,000 civilians. Many thousands more have been wounded.

Formidable challenges face foreign troops in the east, along with an uncertain ally across the border in Pakistan.

NATO is seeking to weaken a host of insurgents, who in eastern Afghanistan also include the independent Hezb-i-Islami group, and push them toward embryonic peace talks with the Afghan government rather than achieving a decisive battlefield victory in this long guerrilla war.

But it's an open question as to whether Pakistan will use whatever influence it may have to bring the Haqqanis off the battlefield, because Pakistan and the United States do not have the same interests in the region.

The network is led by the battle-hardened but ailing Jalaluddin Haqqani, although his son Sirajuddin is its operational leader.

It is considered close to both al Qaeda and the Pakistani security establishment. It was one of Pakistan's most valuable assets during the Soviet occupation of Afghanistan in the 1980s, and Pakistan acknowledges it maintains contact with the group.

Pakistan wants to regain influence in Afghanistan by using Afghan Taliban militants and the Haqqani network taking shelter in Pakistan. The United States needs to eliminate or neutralize those same militants and their sanctuaries so it can withdraw its combat troops from Afghanistan by the end of 2014.

So, Clinton may have demanded more help in facilitating peace talks, even if the Haqqanis so far have seemed irreconcilable.

"We asked very specifically for greater cooperation from the Pakistani side to squeeze the Haqqani network and other terrorists, because we know that trying to eliminate terrorists and safe havens on one side of the border is not going to work," she said. It's unclear exactly what Pakistan is willing to do.

In the end, it's in Islamabad's interests to have a pro-Pakistani government in Kabul, and they see groups like the Haqqanis as a means of ensuring that. A potent fighting force of pro-Pakistani militants could bull its way into, or even topple, a fragile Afghan government after NATO withdraws the bulk of its combat troops.

"In the long run, the United States will have to get realistic about the region," wrote Christophe Jaffrelot, a senior research fellow at the Center for International Studies and Research at Sciences Po in Paris.

"It might just have to admit that the Pakistanis do not believe that the two countries share interests, even if Washington continues to pretend that they do."

(Additional reporting by Andrew Quinn and Missy Ryan in WASHINGTON; Editing by Raju Gopalakrishnan and Paul Tait)