Pro-Taliban fighters have taken control of territory in large parts of Afghanistan and Pakistan, where they have pushed to within 100km of the capital, Islamabad.
"We know that each of your countries is struggling with the extremists who would destabilise and undermine democracy," Clinton said.
Zardari promised to aid the US and Afghanistan in the battle against al-Qaeda and Taliban fighters.
"We stand with our brother Karzai and the people of Afghanistan against this common threat, this menace, which I have called a cancer," Zardari said.
Karzai said Pakistan and Afghanistan "are conjoined twins," adding: "Our suffering is shared."
The two leaders met Barack Obama, the US president, for a three-way summit later on Wednesday.
Anthony Cordesman, a former senior intelligence analyst at the US defence department, told Al Jazeera the stakes are high for the US, and for Obama, in securing stability in the region.
"If you lose Afghanistan, it essentially becomes a sanctuary for [Osama] Bin Laden, for extremist movements, a training ground [and] a centre of terrorism in the region basically throughout the world," he said.
"As far as Pakistan goes, the situation is even worse. It's a nuclear power, you have no idea where the weapons may end up, you see it potentially being used as a lever, a centre of power to put pressure on countries throughout the Islamic world and again as a centre of terrorism."
Deaths regretted
The Washington meeting comes amid anger in Afghanistan over the deaths of more than 100 civilians, reportedly in a US raid.
Clinton said she deeply regretted the deaths and promised to try and avoid them in the future.
Obama has pledged to deal with the situation in the two countries with a joint strategy that will deploy about 20,000 more troops to Afghanistan and hand billions of dollars in aid to Pakistan.
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Pro-Taliban fighters remain in control in
parts of northwest Pakistan [EPA] |
Afghanistan is struggling with rising attacks by Taliban fighters, some of whom use Pakistan as a base from which to launch attacks.
The summit aims to promote co-operation between the two neighbours, but has been overshadowed by US concerns about Pakistan's stability.
Richard Holbrooke, the US special envoy to Pakistan and Afghanistan, insisted on Tuesday that Pakistan was not a "failed state" and said Washington was committed to supporting the government in Islamabad.
"Pakistan's of such immense importance to the United States, strategically and politically, that our goal must be unambiguously to support and help stabilise a democratic Pakistan headed by its elected president, Asif Ali Zardari," he told congress.
Holbrooke also said that Pakistan must start to "show results" in its efforts to address the security situation along the border with Afghanistan.
"Pakistan must demonstrate its commitment to rooting out al-Qaeda and the violent extremists within its borders," he said.
Relations between Islamabad and Kabul have been strained over the security situation, with Afghan officials accusing elements within Pakistan's military and intelligence services of supporting the violence and doing little to stop fighters crossing the border.