Washington has pledged to provide Islamabad with about $7.5bn in economic aid over the next five years to tackle the violence along its border with Afghanistan.
However, the aid bill passed by the US congress requires the White House to certify that Islamabad is tackling terrorism and the intelligence services are not aiding armed groups in the country's northwest.
Last month, Mullen told CNN television that there were "indications" that elements within Pakistan's intelligence agencies were "supporting" fighters both on the border with Afghanistan and India.
Speaking after talks with Shah Mahmood Qureshi, Pakitsan's foreign minister, on Tuesday, Holbrooke did not address Zardari's comments, but said that the two countries must work together.
"We did talk about drones and let me be very frank. There's a gap"
Shah Mahmood Qureshi,
Pakistani foreign minister
"The United States and Pakistan face a common strategic threat, a common enemy and a common challenge and, therefore, a common task," he said.
Qureshi said that despite the shared interests along the Afghan border, there remained "gaps" over certain issues, including suspected US drone attacks in Pakistan's border areas
There are believed to have been 37 drone attacks since August 2007, killing about 360 people.
The US does not confirm raids but the military in neighbouring Afghanistan and the Central Intelligence Agency (CIA) are both known to use the unmanned aircraft.
"We did talk about drones and let me be very frank. There's a gap. There's a gap between us and them, and I want to bridge that gap," Qureshi said.
"My view is that they are working to the advantage of the extremists. We agree to disagree on this.
"We can only work together if we respect each other and we trust each other. There is no other way. Nothing else will work."Regional strategy
Pakistan has complained that the attacks violate its sovereignty and have increased resentment of the government in some areas. The Pakistani Taliban has threatened to carry out two attacks a week until the strikes stopped.
Barack Obama, the US president, recently unveiled a strategy for the region which aims to take a joint approach to deal with the problems in both Afghanistan and Pakistan.
Thousands more troops have been pledged for Afghanistan, as well as 4,000 advisers to train the military, alongside the economic assistance for Pakistan.
Holbrooke and Mullen are expected to travel to India after Pakistan.
Relations between New Delhi and Islamabad have been increasingly strained since the Mumbai attacks in November last year.
India blames a Pakistan-based group for the three-day rampage in the city that left nearly 180 people dead.