More than 700 militants have been killed since the operation began last week, General Abbas said. “The militants are on the run,” he said.

The general’s claims are impossible to verify because reporters and other independent observers have been excluded from the area. There was no indication, for instance, that the fight to wrest the district capital, Mingora, from Taliban fighters had begun. Pakistanis reached earlier this week said the militants had retained all the territory they held in Swat when the operation began.

The exodus, if it proves to be as large as the government says, would be one of the largest migrations of civilians in the region since the partition of India and Pakistan in 1947, when as many as 14 million people left their homes for one of the newly independent countries.

The Pakistani government and relief agencies have set up a string of camps and food distribution centers in the area, but not nearly enough to accommodate all the people who need them. On Monday, Prime Minister Yousaf Raza Gilani appealed to foreign countries to help Pakistan deal with the human tide. On Tuesday, the United Nations said it was sending 120 tons of emergency supplies to Pakistan to help with the flow of refugees.

For all the turmoil unfolding here, a mood of confidence has settled on Islamabad, the capital, since the operation began last week, not necessarily over the chances of its success, but for what appears to be a change of heart in the Pakistani Army. The army, historically the most influential institution in the country, has for years acquiesced in the advance of the Taliban insurgency, which has taken control not just of the Swat Valley, but also of the vast region known as the Federally Administered Tribal Areas.