President Bush said that the US wanted to help Pakistan
US President George Bush has said he wants to help Pakistan protect itself.
He was speaking moments before his first meeting with Pakistani President Asif Ali Zardari at the sidelines of the UN General Assembly in New York.
Mr Bush did not refer directly to controversial US strikes in Pakistan that have caused bilateral tension.
Meanwhile, the US has denied reports that an unmanned US drone crashed in Pakistan after being shot down by Pakistani troops and tribesmen.
There is growing anger in Pakistan at US forces in Afghanistan violating Pakistani sovereignty.
President Bush said before the meeting: "Your words have been very strong about Pakistan's sovereign right and sovereign duty to protect your country, and the United States wants to help."
The US is watching closely how Pakistan reacts to the Marriott attack
Details of what was said during the discussions between the two presidents have not yet been made available.
The US has launched several attacks on militant targets in Pakistan recently.
Details about Tuesday's incident involving the suspected drone are still unclear.
Pakistani intelligence sources said a drone came down in the village of Jalal Khel in South Waziristan, close to the Afghan border.
They said local tribesmen and Pakistani troops had shot it down.
But a senior US official challenged the account.
"We're not aware of any drones being down," an unnamed official told the Associated Press news agency.
Correspondents say the incident is likely to add to the US-Pakistan tension.
The nations have been in deep disagreement since 3 September when the US conducted its first ground assault in Pakistani territory on what it said was a militant target in South Waziristan.
The Pakistani government reacted with fury at the unauthorised incursion in which they said US troops killed 20 innocent villagers.
On two occasions since then Pakistani troops are reported to have fired warning shots to thwart US forces trying to cross the border.
US military officials have complained that militants operate from safe havens in Pakistan from where they attack international and Afghan troops in Afghanistan.
They say that if they brief Pakistan about where they want to attack militants, elements in Pakistan's intelligence services sympathetic to the militants tip them off to help them escape.
The BBC's Chris Morris in Islamabad says that cross-border co-operation was high on the agenda when Mr Zardari and Mr Bush met at the UN.
In a recent interview on American television, Mr Zardari again insisted that only Pakistani forces were authorised to operate on Pakistani soil.
Our correspondent says Mr Zardari cannot accept any military activities which will increase the mood of anti-Americanism in his country and from his perspective make the fight against militancy more difficult.
Also on the agenda was the bombing of the Islamabad Marriott hotel that left more than 50 people dead.
A little-known group calling itself the Fidayeen-e-Islam said it carried out the bombing. It has called for an end to all American involvement in Pakistan if further attacks are to be avoided.
The US state department said the bomb showed the need for the US, Pakistan and Afghanistan "to work and redouble our efforts to counter extremism".
The BBC's Kim Ghattas in Washington says the US is watching closely to see how Islamabad deals with the aftermath of the Marriott attack.
Pakistan's government has promised raids in some "hotspots" near the Afghan border.
But the US would like to see Pakistan take a more aggressive military approach on the ground, and rethink its unpopular peace deals with the militants.