The latest actions will please Washington, which is urging Pakistan to crack down on militants blamed for rising violence at home and in Afghanistan.
Since fighting broke out Tuesday, thousands of men, women and children have fled Swat's main town of Mingora and surrounding districts, fearing an imminent major military operation. The government said it believes refugees could reach 500,000.
"It is an all-out war there. Rockets are landing everywhere," said Laiq Zada, a 33-year old who fled the valley late Tuesday and was now in a government-run tent camp out of the danger zone. "We have with us the clothes on our bodies and a hope in the house of God. Nothing else."
The clashes followed the collapse of a 3-month-old truce in Swat that was widely criticized in the West as a surrender to the militants, who had fought the army to a standstill in two years of clashes that saw hundreds of civilian casualties.
It is uncertain whether the Pakistani public has the stomach for a long battle. The truce gave militants time to rest and reinforce their positions and any operation would involve fierce fighting in urban areas and would likely cause significant civilian casualties and property damage.
The Swat Taliban are estimated to have up to 7,000 fighters against some 15,000 troops who until recent days had been confined to their barracks under the peace deal.
The military said Wednesday's offensive killed about 35 militants positioned near emerald mines in the Swat Valley and 27 in neighboring Buner, where troops have halted a Taliban push toward the capital Islamabad.
The Taliban killed two soldiers with a roadside bomb and two more in an assault on a power plant near Mingora, a military statement said.
"Armed militants have come down from their hide-outs into the cities and have occupied civil houses and government buildings" as well as planting bombs to target both troops and civilians, it said.
The militant casualty figures could not be verified independently, and there was no official word on deaths or injuries among civilians.
An Associated Press reporter in Mingora said gun and mortar fire started Tuesday and continued through the night into Wednesday. An intelligence official said helicopters and mortar teams were pounding militant positions in Mingora and other parts of Swat.
"The situation is very tense there. Taliban are present at the homes of local residents. They are also present at strategic positions. They are using light weapons to ambush troops," said the official on condition of anonymity as he was not authorized to speak to media.
Army spokesman Maj. Gen. Athar Abbas declined to say whether the events heralded the start of major operations, saying only that "all the contingency plans are worked out" for carrying one out.
In recent days, however, there have been signs the mood toward the Taliban is changing. Many politicians, commentators and religious leaders now say the movement's true nature was exposed by its refusal to go along with the peace deal despite the government's best efforts.
Pakistan agreed to a truce in the valley in February. As part of the agreement, the government imposed Islamic law last month in the region in hope insurgents would lay down their arms -- something they did not do.
The developments brought Islamabad's faltering campaign against extremism into sharp focus as President Asif Ali Zardari prepared for talks Wednesday in Washington with Obama and Afghan President Hamid Karzai on how best to counter an increasingly overlapping spectrum of extremist groups behind surging violence in the neighboring countries.
The Obama administration hopes to build a strong and lasting regional alliance, linking success in Afghanistan with security in Pakistan. Toward that end, the administration is encouraging Pakistan to confront -- not make peace with -- the Taliban and other militants.
"We need to put the most heavy possible pressure on our friends in Pakistan to join us in the fight against the Taliban and its allies," Richard Holbrooke, the U.S. special representative for Afghanistan and Pakistan, told a congressional committee Tuesday. "We cannot succeed in Afghanistan without Pakistan's support and involvement."
In an interview with CNN, Zardari defended his country's ability to fight the militants within its borders. "It doesn't work like that. They can't take over," he said. "How can they take over?"
Fearing war could consume the region, thousands fled Mingora on Tuesday. Refugees clambered onto the roofs of buses after seats and floors filled up. Children and adults alike carried belongings on their heads and backs.
"I do not have any destination. I only have an aim -- to escape from here," said Afzal Khan, 65, who was waiting for a bus with his wife and nine children. "It is like doomsday here. It is like hell."
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