By Susannah Price BBC correspondent in Islamabad

As the US-led operation to hunt down al-Qaeda and Taleban suspects in Afghanistan continues, there are increasing suspicions that many have now crossed the border into neighbouring Pakistan.

They can expect to find sanctuary on the other side, where the local people have close ethnic and cultural ties with the Taleban, and where, traditionally, the Pakistani Government has little authority.

Maybe under America's security definition these Pakistanis are a threat, but a Pakistani government can't see it like that

Columnist Naseem Zehra

The Pakistani authorities have launched their biggest operation ever in the tribal areas to hunt down the Islamic extremists.

And tribesmen have been outraged by reports that American forces have been helping the Pakistani troops.

Last month, the caretaker at a madrassah - or religious school - run by a former Taleban cabinet minister said American troops had accompanied Pakistani forces on a raid on the complex.

The school was closed and nothing was found.

The tribesmen in the area, known as Waziristan, held a meeting to protest against the American presence - although they deny supporting al-Qaeda.

'America should behave'

And it is not just the local people who are up in arms. The country's religious parties, who were also Taleban supporters, want the Americans out.

Professor Khurshid Ahmed, vice-president of the conservative Jamaat-e-Islami, said it was a question of sovereignty.

"We have no quarrel with America," he said. "But America should behave. If you are powerful it does not mean it should go to your head - this is a recipe for disaster."

Pakistan's troops are stretched

The Pakistani authorities say the American personnel are only engaged in communications. But Islamabad and Washington may have different ideas on who they are targeting.

A local newspaper columnist, Naseem Zehra, said a distinction had to be drawn between the true al-Qaeda and the tribesmen who were sympathetic to the Taleban.

"Maybe, under America's security definition these Pakistanis are a threat, but a Pakistani government can't see it like that," she said.

One American report suggested the United States was impatient with the slow progress of operations.

Pakistan says it is doing its best. But the Information Minister, Nissar Memon, said the country's forces were limited by their numbers and by a lack of technology and training.

He pointed out that Pakistan was deploying many troops on its eastern border with India, where tension is mounting.

American praise

Publicly at least, the Americans are full of praise for the Pakistani efforts.

The US Assistant Secretary of State for South Asian Affairs, Christina Rocca, visited Islamabad on Wednesday after going to Delhi and spoke of the wonderful co-operation Washington had received from Pakistan.

There are suggestions that last week's suicide attack in Karachi that killed 15 people, including 11 French nationals, was the work of al-Qaeda.

And Pakistan, which joined the American-led coalition after 11 September, is worried about other such attacks.

But its close relationship with America, unless handled sensitively, could lead to a backlash at home.