Pakistan's president reiterated his welcome for Washington's new strategy, in a speech to parliament in Islamabad on Saturday.
Asif Ali Zardari said Mr Obama's offer of development aid for border areas in Pakistan was an endorsement of his own government's counter-extremism policy.
Pakistan's leader also said his country would not allow use of its soil for terrorist activity, and would not let anyone violate its sovereignty.
Afghan leader welcomes US review
But he did not specifically criticise US missile attacks on Pakistani territory as he has done in the past.
Cross-border operations by US-led forces have angered Pakistani authorities in recent months.
In Kabul, Mr Karzai told journalists he was "in full agreement" with the strategy.
"It is exactly what the Afghan people were hoping for, and we're seeking," he said.
"Therefore, it has our full support and backing... and we'll be working very, very closely with the US government to prepare for and to work on implementing all that was laid out in this strategy.
He added: "This is better than we were expecting, as a matter of fact."
On Friday, Mr Obama said growing radical forces in Afghanistan and the border area in Pakistan posed the greatest threat to the American people and the world.
He painted a bleak picture of the situation, with insurgents increasing their control of territory in the region around the Afghan-Pakistan border - which he termed "the most dangerous place in the world" for the American people - and attacks rising.
He said American strategy must relate directly to the threat posed to the Americans by al-Qaeda and its allies - who, he reminded his listeners, were behind the 9/11 attacks on American soil eight years ago.
Hours after the speech, senior US military officials spoke of alleged links between Pakistan's military intelligence, the ISI, and militants on the country's borders with both Afghanistan and India.
Gen David Petraeus, the head of US Central Command, said that if such links undermined operations against the militants, they would damage US efforts to build trust in the region.
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