(Updates death toll, adds background, detail)

ISLAMABAD, July 23 (Reuters) - Pakistan's armed forces killed at least 35 militants in North Waziristan on Monday, two days after U.S. President George W. Bush said he was "troubled" by reports al Qaeda was gaining strength in Pakistani tribal areas.

The deaths, in fighting that was still under way, brought the number of militants killed since Saturday night to 54.

Military spokesman Major-General Waheed Arshad said the latest clashes centred on the town of Mir Ali, where heavy exchanges of fire broke out after militants fired rockets at an army checkpoint overnight.

"We have reports that 35 militants have been killed since Sunday night and fighting is still on in Mir Ali," Arshad told Reuters.

Nineteen militants and seven soldiers have been wounded, he added.

Intelligence sources in Waziristan said the army was using artillery to pound militant positions.

Pakistan's Waziristan region has long been regarded as a safe haven for al Qaeda and Taliban militants sheltered by their local Pashtun allies.

Pakistani authorities struck a deal with the local militants last September in a bid to isolate foreign militants and curb cross-border incursions into Afghanistan.

But the militants scrapped the deal last week and launched attacks in Waziristan, adding to general concern that the security situation in Pakistan was deteriorating.

Bush, in his taped weekly radio address, said President Pervez Musharraf recognised the failings of the North Waziristan agremeent and was taking action.

A U.S. intelligence report made public this week found a "persistent and evolving" threat to the United States from Islamic militant groups, especially Osama bin Laden's al Qaeda which it said had become entrenched in North Waziristan.

U.S. officials have said the United States never ruled out any options when it came to attacking al Qaeda or the Taliban.

Pakistan rejected the statements as "irresponsible and dangerous" and said only its own troops could carry out counter-terrorism actions on Pakistani soil.

But Musharraf's problems go beyond Waziristan.

Islamist militants have launched suicide bomb attacks across the country to avenge the storming of a radical mosque in the capital, Islamabad, this month.

More than 180 people, mostly police and soldiers, have been killed in such attacks since the operation against Islamabad's Lal Masjid, or Red Mosque, began on July 3. The government said 102 people were killed in the siege and the storming of the mosque on July 10.

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