In Washington, even Republican members of Congress who had long been strong supporters of the Afghan war and Mr. Karzai, were scathing in their denunciation of him in recent days. Senator Lindsey Graham of South Carolina, who has visited Mr. Karzai repeatedly and has long been involved with Afghanistan policy, expressed “disgust and resentment” over the Afghan’s comments, in remarks quoted on Foreign Policy magazine’s Web site. He added: “I am perfectly capable of pulling the plug on Afghanistan.”

That last statement was an offhand reference to the negotiations now under way to determine the size and shape of an American military presence in Afghanistan past 2014, and perhaps to the billions in dollars of future American aid already committed to the country.

One senior Obama administration official said Wednesday that commanders on the ground were taking appropriate steps given the circumstances. The official, who spoke on condition of anonymity to discuss negotiations, said that many in the administration were “obviously unhappy” with Mr. Karzai’s comments, but insisted the latest tensions would do little to alter the current military assistance plan for Afghanistan.

Still, some Afghan leaders have expressed concern that American budgetary concerns, coupled with a worsening political relationship between the countries, could lead the United States to reduce or even remove its support.

In Kabul, both Afghan vice presidents met with Mr. Karzai for two hours Wednesday morning, while a group of representatives from 14 political parties — most of them opposition groups but several with members in government — held a news conference to denounce the president’s stance.

“All these remarks may destroy our relations with the international community, and especially America, and lead to the isolation of Afghanistan again,” said Faizullah Zaki, the spokesman for Gen. Abdul Rashid Dostum, the powerful Uzbek leader and warlord who campaigned for Mr. Karzai in his 2009 election and later fell out with him. “We are calling on the president to stop doing this because we believe it is not in our national interest.”

In the American threat advisory issued Wednesday, General Dunford expressed concerns about the strain between the countries, saying, “We’re at a rough point in the relationship.” He said the contretemps could encourage insurgents, given that the Taliban and other groups “are also watching and will look for a way to exploit the situation — they have already ramped up for the spring.”

In the latest outbreak of violence, which Afghan officials attributed to the Taliban, a suicide bomber on Wednesday targeted a crowd after a match of buzkashi, or Afghan polo, in northern Kunduz Province. The attack killed the police chief, Abdul Qayoum Ibrahimi, his son, his father and seven other people. Mr. Ibrahimi was the brother of the speaker of the Afghan Parliament, Abdul Rauf Ibrahimi, and of Abdul Latif Ibrahimi, a presidential adviser. They were not present, but their father was also among the dead.