WASHINGTON - The U.S. House of Representatives on Thursday approved tripling U.S. aid to Pakistan to about $1.5 billion a year for each of the next five years in a key part of a strategy to combat extremism with economic and social development.

The bill also includes military aid with conditions that require the Obama administration to certify that Pakistan remains committed to combating terrorist groups -- a provision that was criticized by the key U.S. ally in South Asia.

The annual funding of about $1.5 billion a year for each of the next five years, includes money for Pakistani schools, the judicial system, parliament and law enforcement agencies.

The action came the same day that U.N. Secretary-General Ban Ki-moon appealed to major donors for more funding for Pakistan, saying it was at risk of a spiraling secondary crisis without more international aid.

The bill, which includes $400 million in annual military aid for 2010-2013, also passed as Pakistan's military opened a second front against domestic Taliban militants that U.S. officials fear could destabilize nuclear-armed Pakistan.

Fighting in the Bannu district of the Waziristan tribal region flared up on Thursday as the Pakistani military was completing the last stages of an operation to clear Islamist fighters from the Swat valley, near Islamabad.

An amendment to the legislation, which must still be harmonized with a similar bill in the U.S. Senate, sets up so-called Reconstruction Opportunity Zones in border areas of Pakistan and Afghanistan, from which textiles and other items can be exported duty-free to the United States.

The zones represent an effort by the Obama government to combat al-Qaeda and Taliban recruitment of insurgents by creating jobs for unemployed youth in underdeveloped parts of the two countries.

Support in Congress for aid for Pakistan will strengthen the resolve of the Pakistani people and government in confronting violent extremists and terrorists, said Pakistan's ambassador in Washington, Husain Haqqani.

He also said his government was unhappy about the conditions tied to some of the aid.

Some conditional language that has been included in the aid bill is not conducive to promoting the objectives of counter-terrorism cooperation, the ambassador said, adding that he hoped the Senate would remove those terms when they complete passage of the aid package.

But Howard Berman, chairman of the House of Representatives Foreign Affairs Committee, said Congress was simply asking Pakistan to follow through with the commitments it has already made.

In the process, we lay down an important marker that Congress will no longer provide a 'blank check,' he said in a statement.

On Wednesday, Richard Holbrooke, the U.S. envoy to Pakistan and Afghanistan told a news briefing he had noticed a dramatic change in Pakistan's attitude toward fighting Islamist extremists during his visit there last week.

(Editing by Bill Trott)