DAVOS, Switzerland — Afghanistan’s president warned yesterday that the whole world could suffer from the “wildfire” of terrorism engulfing his region, a grim message for a meeting of political and business leaders already fretting over the threat of global recession.

Formally opening the World Economic Forum, Hamid Karzai gave a sobering rundown of recent attacks attributed to Islamic extremists — among them the assassination of Benazir Bhutto and bombings in Afghanistan and Pakistan that have killed hundreds, including many children.

With militant violence still on the rise in the two nations six years after the ouster of the Taliban, “it seems like the mutant of extremism is dangerously unleashed across the region,” Mr. Karzai said. The trend “bodes terribly badly for the whole world,” he said.

In an apparent allusion to Pakistan — whose president, Pervez Musharraf, originally supported the Taliban — Mr. Karzai called terrorism “a venomous snake that some among us tried to nurture and befriend at the expense of others, which I hope we realize now was a mistake.”

Mr. Musharraf, now an American ally in the war on extremist groups, has often been accused by Mr. Karzai of not doing enough to shut down sanctuaries for Taliban fighters in Pakistan’s tribal region along the border with Afghanistan.

The Pakistani president is attending the conference in Davos as part of a European tour seeking to reassure the West that he is in control of his country after months of political instability and increased violence in the region. Both leaders held separate talks yesterday with Secretary of State Rice, but there was no indication they would meet with each other. A spokesman for Mr. Musharraf, Rashid Qureshi, told the Associated Press the meeting with Ms. Rice “went very well,” saying there was “total consonance and unanimity of views” on joint efforts to fight terrorism.

How to stem terrorism is one of the themes at this year’s World Economic Forum, along with dealing with climate change, implementing a workable peace process in the Middle East, and discussing how technology is ushering in a new age of social networking that knows no borders.

Still, with many participants watching stock markets slump and sharing the realization that economic downturn can breed political turmoil, the main focus yesterday was on the chances for worldwide recession.

Ms. Rice, in a nod to the economic anxiety, told an audience of chief executives, politicians, and others that the American economy is resilient and will remain an “engine of growth.”

She urged the world to “have confidence in the underlying strength of the global economy — and act with confidence on the basis of the principles that lead to success in today’s world.”

But many leading participants shared the view that the world cannot escape the effects of America’s economic slowdown, marked by the subprime mortgage crisis, loss of business confidence, poor corporate profits, and a sharp drop in stock prices.

“We’re in Round 1 or 2. This is a 15-round fight,” the governor of the Central Bank of Mexico, Guillermo Ortiz, said, suggesting the worst might yet be coming.