Gilani, who will be in the US for three days, said in turn that the country's battle against Taliban and al-Qaeda fighters was "a war ... against Pakistan, and we'll fight for our own cause".
However he later said in an interview with CNN that Monday's missile strike was "certainly'' a violation of Pakistan's sovereignty "if it is proved".
The White House later said that Bush had also offered Pakistan $115 million over two years in food aid, of which $42.5 million will be available over the next six to nine months, during the talks.
Al Jazeera's Rob Reynolds in Washington says the attitude within US congress towards Pakistan, already a major receiver of US military aid, is to have more strings attached to any such aid in the future in a bid to link funds with more concrete results and accountability in the nation's battle against fighters in the tribal regions.
This remains a conundrum, however, for Pakistan as the government wishes to negotiate with such fighters and not engage in military action against them, our correspondent adds.
Monday's missile attack on a religious school in Azam Warsak village in the district of South Waziristan killed six people, including three foreigners, Pakistani intelligence officials told the Reuters news agency.
There was no immediate claim of responsibility, however the incident follows a series of recent raids, apparently by US aircraft, against fighters in the region which have strained relations between the two nations.
US state department and White House officials told Al Jazeera they had no information on the incident.
And both US forces based in Bagram base in Afghanistan and members of the International Security Assistance Force (Isaf), the Nato-led security mission in Afghanistan, denied involvement.
The talks come at a time of tension between the two countries, as US officials say the new Pakistani government's pursuit of peace deals with tribes along the porous Pakistani-Afghan border has allowed fighters to regroup and stage attacks on US forces in Afghanistan.
Earlier on Monday, Dana Perino, the White House spokeswoman, said that Bush believed that Pakistan recognised the fighters "are a threat to the Pakistanis themselves - not just to the United States or others".
|Pakistani troops have been struggling to
contain violence in border regions [AFP]
"Does the president think they are doing enough? I think the president thinks we all need to be doing more," she said.
Bush had said ahead of his meeting with Gilani that he was "troubled" by the movement of fighters from Pakistan to Afghanistan and would discuss the threat with Gilani, who is making his first Washington visit since Pakistan formed a new coalition government in March.
Pakistani officials say they are working to forge agreements that would require tribes to surrender their weapons, withdraw support for foreign fighters and end attacks across the border from the tribal region, where Osama bin Laden, the al-Qaeda leader, is thought to be hiding.
But the government has also resisted proposals to allow US or other foreign troops in to the border region.
There has been growing speculation that the US is prepared to launch military "hot pursuit" raids into the region against fighters.
Last month a US air raid killed 11 Pakistani border troops, which led to angry protests from the Pakistani government.