In a Rose Garden appearance arranged to show warmth and unity, the bickering leaders of Pakistan and Afghanistan shook hands with President Bush but not with each other.

Pakistani President Gen. Pervez Musharraf and Afghan President Hamid Karzai, whom Bush considers key bulwarks against Islamic radicalism in a volatile region, barely looked at one another as Bush appealed for cooperation against the common enemy of terrorism.

"These two men are personal friends of mine," Bush said in a brief Rose Garden appearance before Wednesday's light dinner of soup, sea bass and salad. "They are strong leaders who have an understanding of the world in which we live. They understand that the forces of moderation are being challenged by extremists and radicals."

The meeting was a command performance for leaders who have joined their fortunes to Bush's anti-terror drive since the Sept. 11, 2001, attacks but who for months have picked at one another's efforts to fight terrorists along their long, remote, mountainous border.

They actually did shake hands before joining Bush in appearing before reporters, National Security Council spokesman Frederick Jones said Thursday.

After the private meal, the White House issued a bland statement that called the session a "constructive exchange" but outlined no new agreements or initiatives. The White House did not make any officials available for questions.

"They committed to supporting moderation and defeating extremism through greater intelligence sharing, coordinated action against terrorists, and common efforts to enhance the prosperity of the people of Afghanistan and Pakistan," the statement from press secretary Tony Snow said.

Afghanistan's ambassador to the United States, Said Jawad, said the dinner ran into overtime — two and a half hours instead of the scheduled one — and ended on a good note. He said Karzai and Musharraf agreed to hold two joint tribal councils, gathering tribal leaders from both sides of their border, and to meet again soon.

Jawad said the discussion was frank, but he did not say whether Bush directly asked his guests to knock off their sniping in public.

Snow, speaking to reporters Thursday, said the two leaders agreed on new ways to fight terror and address root causes of terrorism. Snow would not say whether they agreed to a verbal cease-fire.

Bush's three-way dinner party, just weeks before the November congressional elections, came as he works to persuade voters that Republicans are best able to guide the U.S.-led war against terrorism. He faces declining American support for both the U.S.-led war in Iraq and the U.S. military commitment in Afghanistan.

Afghan officials claim that Pakistan lets Taliban militants hide out and launch attacks into Afghanistan. Musharraf says Karzai has bad information and notes that Pakistan has deployed 80,000 troops along the porous border.

Karzai says Musharraf turns a blind eye to hatred and extremism being bred at Islamic schools in Pakistan. At one point, Musharraf said Karzai is behaving "like an ostrich," refusing to acknowledge the truth and trying to shore up his political standing at home.

Right up to Wednesday night's White House dinner, they also have pointed fingers at one another over Al Qaeda's Usama bin Laden and other terror leaders. Each says bin Laden isn't hiding in his country and suggests the other might do more to help find him.

The heated accusations had put the White House in the middle, and Bush thought it was time to clear the air.

Standing between the pair, Bush emphasized "the need to cooperate, to make sure that people have got a hopeful future" in both countries.

The Afghan and Pakistani leaders stood stiffly on either side of Bush as he spoke without notes or a lectern. Musharraf was tightlipped, hands clasped awkwardly before him. Karzai nodded agreeably as Bush spoke. Neither of the foreign leaders spoke.

"Today's dinner is a chance for us to strategize together" and find common solutions, Bush said.

Speaking in London Thursday, where he traveled after his U.S. visit, Musharraf said, "The meeting that I held with President Bush and Hamid Karzai last night was very good. It was decided that we should have a common strategy. We have to fight terrorism. We have to defeat it, defeat it jointly."

The session came as Afghanistan suffers its worst reversals since the U.S.-led ouster of the extremist Taliban regime nearly five years ago.

The Taliban militants have regrouped and launched an offensive earlier this year whose strength and organization took Afghan and U.S. officials by surprise. They have adopted methods commonly used by militants in Iraq: suicide bombings, ambushes and beheadings.

Illegal opium production has risen yearly despite billions of dollars spent to suppress it, and Afghanistan is now the source of more than 90 percent of the world's supply.