Mr Bush is due to host president Pervez Musharraf of Pakistan and Hamid Karzai of Afghanistan for a peace-making dinner at the White House amid worries that their testy relations are hurting efforts to quell surging Taliban violence and to hunt down terrorist mastermind Osama bin Laden.
"Certainly we understand that there are tensions between the countries, and we're going to do whatever we can, that they want us to do, to help resolve them," White House spokesman Tony Snow said.
The three leaders were to make a brief public appearance in the White House Rose Garden before disappearing behind closed doors for their dinner.
Mr Snow seemed to hesitate when asked whether Mr Bush believed that Mr Musharraf, facing criticisms that he is not doing enough to quell violence threatening Afghanistan, was doing everything in his power on that front.
"I don't know how you define 'everything in his power.' How would I define it?" said Mr Snow. "He is making serious efforts. The president's satisfied with the efforts he's made and supports them."
Mr Bush met with Mr Musharraf on Friday and with Mr Karzai on Tuesday.
Mr Musharraf used an interview with the Canadian Broadcasting Corporation to fire the latest salvo in his war of words with Mr Karzai, accusing him of being "concerned more about himself than about Afghanistan."
"We should work together, but I'm afraid he is not being honest about everything," the Pakistani leader said.
A day earlier, Mr Musharraf denied claims that Taliban leader Mullah Omar had found refuge on Pakistani soil and charged that it was Afghanistan that was not doing enough to battle extremism.
President Bush sought to play down suggestions of Afghan-Pakistani tensions, denying disagreements had undermined efforts to stabilise Afghanistan, where US forces have faced their bloodiest year since toppling the Taliban in late 2001.
“It's in President Karzai's interest to see bin Laden brought to justice. It is in President Musharraf's interests to see bin Laden brought to justice. Our interests coincide," Mr Bush said.
Asked about the tensions between Islamabad and Kabul, Mr Karzai repeatedly referred to Mr Musharraf as "my brother" and praised the US role in "helping both countries" but did not back down from previous criticisms.
"We know our problems. We have difficulties. But Afghanistan also knows where the problem is, in extremism, in madrassas preaching hatred, places by the name of madrassas preaching hatred," said Mr Karzai.
That was an apparent reference to past criticisms of Pakistan for not doing enough to root out extremism from those Islamic religious schools.
Mr Karzai also expressed skepticism about a peace deal between Pakistan's government and tribal chiefs in a remote Afghan-Pakistani border region that Kabul has said may be a haven for al-Qaeda terrorists and Taliban fighters.
"But, generally, we will back any move, any deal that will deny terrorism a sanctuary in North Waziristan or in the tribal territories of Pakistan," Mr Karzai said.
Mr Musharraf, who has added spice to his encounters with Bush after claiming the United States threatened to bomb Pakistan back to the "Stone Age" if it failed to join the "war on terror" in 2001, raised more eyebrows Tuesday.
He said on CNN that he believed the Iraq war "has made the world a more dangerous place," contradicting Bush's own claims that it had made America safer.
The US president has come under renewed pressure, with barely more than a month before critical November US legislative elections, to step up the search for bin Laden, the architect of the September 11, 2001 attacks.