Prime Minister Yousuf Raza Gilani, a senior official from the party of slain opposition leader Benazir Bhutto, made the comments when Bush telephoned him on Tuesday to congratulate him on taking office.
Meanwhile, former premier Nawaz Sharif told two US envoys on Tuesday that the new government would review President Pervez Musharraf's anti-terror policies and focus on what was best for Pakistan.
Mr Gilani told Bush 'that Pakistan would continue to fight terrorism in all its forms and manifestations since it is in Pakistan's own national interest,' said a statement issued late Tuesday by his office.
'However, he said that a comprehensive approach is required in this regard, specially combining a political approach with development programmes,' it added.
Mr Gilani said that Pakistan was 'committed to maintaining long-term close ties with the USA.'
Mr Gilani was due to meet with visiting Deputy Secretary of State John Negroponte and Assistant Secretary of State Richard Boucher later on Wednesday, a day after they met Mr Musharraf and Mr Sharif, his office said.
Analysts said the US visit was designed to woo the new government and smooth relations between it and Musharraf, amid fears that instability in the nuclear-armed nation will hurt efforts to tackle Islamic militancy.
Pakistan has been a key ally in the fight against Al-Qaeda and Taleban militants since 2001.
More than 600 people have died in militant-related violence this year.
Previous attempts at peace deals with militants in the tribal belt bordering Afghanistan have collapsed with further bloodshed and caused alarm in Washington.
Mr Sharif said he told Negroponte that a parliamentary committee would look at Mr Musharraf's policies on curbing militancy, saying the new government wanted to tackle extremism but did not want the country to become a 'murder-house'.
Meanwhile Mr Bush used his authority to exempt Pakistan from a law that restricts funding countries where the legitimate head of state was deposed by a military coup, as in Pakistan, the White House said on Tuesday. --- AFP