The fighting, which erupted a week ago, will likely put a strain on a peace deal between the Pakistani government and militants seeking to impose the Taliban-style Islamic law of Sharia in the picturesque region, according to Reuters.
Three members of the Pakistani intelligence agency, the ISI, were among the 14 soldiers killed last week.
The army said it came up with the casualty figure by intercepting militants' radio communication, the BBC reported.
The military also said it plans to launch an all-out offensive against the militants soon, ending a fragile deal that the two sides signed two months ago.
"More troops are coming and we will launch a major operation and we will go after the militants in their strongholds," local military commander Brig. Zia Bodla told reporters.
Bodla said the army was forced to act in Swat because militants were "attacking the security forces, setting ablaze schools and harming the local population. We defused eight bombs on Saturday alone," he said, according to the Agence France-Presse.
The militants have destroyed four girls' schools and set fire to a health office, a forestry office and several bridges.
Pakistan is under mounting international pressure to crack down on Taliban and al-Qaida militants in northwestern Pakistan and the adjoining, semi-autonomous tribal belt.
Under the terms of the May deal, the government agreed to gradually pull out troops and introduce an Islamic justice system. In exchange, the rebels said they would halt attacks and surrender arms, the AFP reported.
The militants have accused the government of reneging on the terms of the peace deal and have vowed to keep fighting until troops leave the valley.