ISLAMABAD , Pakistan ( CNN ) -- Pakistan 's military is pounding Taliban targets in the country 's Swat Valley , trying to clear militants who control parts of the district 's main city , military officials said . Pakistani army trucks transport cannons for the military operation against the Taliban . The Pakistani forces had killed 35 militants in Wednesday 's fighting , the officials said . The officials said there are reports of some civilian casualties in Wednesday 's fighting -- which has been concentrated in Swat 's district capital of Mingora -- but they denied local media reports that 35 civilians died . An eyewitness said he saw the bodies of 15 civilians were being taken from a village near Mingora on Wednesday . Twelve of the dead were children . Taliban militants have laid siege to Mingora , looting banks , attacking army headquarters , the police station , and the main power grid station , the officials said . They are also occupying civilian houses and government buildings in the city center , according to the military . See a map of Taliban-controlled areas » . The fighting has trapped 80 boys inside an orphanage in the city , according to Muhammad Ali , the director of the facility . Another 20 staffers are also holed up inside the four-story building , and they only have enough food for two more days , Ali said . Local government officials issued an evacuation order for the Swat area Tuesday , ahead of the military operation . An estimated 40,000 people have fled Mingora , according to Khushhal Khan , district coordination officer . Government officials warn that the fighting could lead to the exodus of 500,000 civilians . Watch as thousands flee military offensive » . For the last two weeks , Pakistani troops have battled Taliban fighters in Buner and Lower Dir , two districts bordering Swat . Army generals claim to have killed scores of militants . Fighting continues in those two districts , and the operations are `` progressing smoothly , '' the military said Wednesday . Militants struck a girls ' college in the area with rocket fire , partially damaging the building , the military said . Watch conditions in a refugee camp in Pakistan » . Pakistan 's government recently signed a deal that would allow Islamic law , or sharia , in the Swat Valley , in exchange for an end to fighting . The government began its military operation after Taliban militants moved into the Buner district and refused to disarm , in violation of the agreement . Pakistan 's President Asif Ali Zardari will meet with U.S. President Barack Obama and Afghan President Hamid Karzai on Wednesday in Washington . Obama is hoping to build an enduring regional alliance with both countries , enlisting them as full partners rather than treating them as battlefields for U.S. soldiers to fight extremists . Last week , Obama said Pakistan 's government appears to be `` very fragile '' and argued that the United States has `` huge national security interests in making sure that Pakistan is stable '' and does n't end up a `` nuclear-armed militant state . '' CNN 's Samson Desta and Elise Labott contributed to this report .
Pakistani military pounds Taliban fighters , killing 35 in Swat Valley offensive An estimated 40,000 people flee city of Mingora as forces clash . 500,000 civilians expected to flee Swat Valley area as offensive continues . Score: 6 U.S. President Obama Wednesday .