The strongest such outburst came Friday. “Let’s pray for God to rescue us from these two demons,” Mr. Karzai said, apparently holding back tears at a meeting with relatives of the massacre victims, and clearly referring to the United States and the Taliban in the same breath. “There are two demons in our country now.”

Ever since the Koran-burning incident on Feb. 20 and its violent aftermath, the relationship between the two governments has lurched from one crisis to another. American officials have scrambled to run damage control, with President Obama calling Mr. Karzai twice in the past week and apologizing twice in the past month — once for the Koran burning and once for the massacre…

Western diplomats have often viewed Mr. Karzai’s outbursts as playing to the galleries, meant for consumption by his own people only, not as serious statements of policy. But the galleries also include the publics in the United States and its NATO allies, where majorities in nearly every country oppose remaining in Afghanistan, and every new contretemps risks further eroding an already tenuous support…

The relationship is so frayed, however, that Mr. Karzai often is quick to view everything through the prism of presumed American perfidy. When American diplomats meet with his political opponents, he sees it as a sign that they are out to topple him from power — something that has reportedly obsessed him ever since the presidential election in 2009, which the international community saw as widely fraudulent. American officials pressured him into agreeing to a runoff, which in the end his opponents refused.