The coalition said some international troops were killed and wounded in the attack, but did not disclose details.
Late Wednesday, NATO reported that one coalition trooper had been killed in an explosion in southern Afghanistan, but would not say whether the service member died in the Kajaki bombing, or some other incident.
U.S. Gen. John Allen, the top commander of American and NATO forces in Afghanistan, condemned the Kajaki attack, saying it was evidence that the Taliban insurgents had "declared outright war" on the Afghan people. He said that such violence "will only further isolate the Taliban from the process of peace negotiation."
The U.S. has been working to broker talks between the Taliban and President Hamid Karzai's government to end the 10-year war. The insurgents recently said they would open a political office in the Gulf state of Qatar to pursue negotiations but would also continue fighting.
Several current and former U.S. officials said the most substantive give-and-take to date between U.S. and Taliban negotiators could happen in the next week, with the goal of establishing what the U.S. calls confidence-building measures — specific steps that both sides agree to take ahead of formal talks.
However, U.S. intelligence agencies recently offered a gloomy prognosis in their latest Afghanistan report.
The Afghan National Intelligence Estimate warns that the Taliban will grow stronger, using the talks to gain credibility and run out the clock until U.S. troops leave Afghanistan, while continuing to fight for more territory, say U.S. officials who have read the classified document. They spoke on condition of anonymity to describe the roughly 100-page review, an amalgam of the intelligence community's predictions of possible scenarios for the Afghan war through the planned end to U.S. combat in 2014.
The report says the Afghan government has largely failed to prove itself to its people and will likely continue to weaken and find influence only in the cities. It predicts that the Taliban and warlords will largely control the countryside.