The operation unfolded near Wana, in Pakistan's South Waziristan region, just a few miles from the Afghan border, said army spokesman Gen. Shaukat Sultan.
"We believe that 24 suspected terrorists have been killed," he said.
Most of those killed were apparently thought to be Pakistani tribesmen suspected of sheltering the terrorists, but Sultan said that several of the dead were also believed to be foreigners presumed to be al Qaeda members.
The operation follows a weekend announcement that U.S. forces are stepping up a sweep on the Afghan side of the border to capture al Qaeda and Taliban holdouts, including terror chief Osama bin Laden and Taliban leader Mullah Omar.
About 700 paramilitary forces began the operation early Tuesday in Kaloosha, a village about six miles west of Wana, the main town in South Waziristan.
A Kaloosha resident, Qasim Khan, said paramilitary troops exchanged fire with people inside a fortress-like house. It was unclear who was inside, but it was believed to belong to one of seven tribesmen from the Yargul Khel clan accused of harboring al Qaeda and Taliban suspects. The seven have refused to surrender.
"We are not allowed to go out of our homes," Khan told an Associated Press reporter by telephone from the besieged village.
It is the latest in a series of military operations in Pakistan's semiautonomous tribal regions. President Gen. Pervez Musharraf vowed Monday to rid Pakistan's tribal areas of suspected terrorists, and acknowledged for the first time that 500-600 foreigners were sheltering in the region. He appealed to tribal elders for their cooperation in the counterterrorism drive.
His comments came ahead of a scheduled two-day visit to Pakistan and Afghanistan starting Wednesday by Secretary of State Colin Powell. On Monday, police defused a large car bomb outside the U.S. Consulate in the southern city of Karachi just minutes before it was timed to detonate.
U.S. forces in Afghanistan over the weekend announced the start of Operation Mountain Storm, a large-scale sweep to hunt down al Qaeda and Taliban fugitives believed to be hiding in the border region.
Lt. Col. Bryan Hilferty, a spokesman for the U.S. military in Afghanistan, said U.S. forces were involved in searches and patrols in Paktika, the Afghan province bordering South Waziristan. He said American commanders "continue to coordinate and cooperate" with the Pakistanis, but would not say if there were any operations linked to the Wana crackdown.
Paktika Deputy Gov. Sadokhan Ambarkhil told AP he had no information about any military activity on the Afghan side of the border, but that drivers from the border region had told of U.S. forces carrying out an operation Friday. He had no details.
Pakistan is a key ally in the U.S.-led war on terrorism, but has faced criticism because rebels of al Qaeda and Afghanistan's former ruling Taliban regime are believed to still be launching attacks from Pakistani soil.
Mehmood Shah, a government administrator for the tribal areas based in the northwestern city of Peshawar, said Tuesday's operation involved about 700 paramilitary soldiers.
The paramilitary forces blocked a road leading to Kaloosha from Wana and vehicles heading toward the village were turned back. An AP reporter could hear mortar fire.
A cleric appealed for negotiations to end the fighting.
"People should go to Kaloosha to mediate a cease-fire so that ordinary people are saved from bloodshed," Bazid Khan said via loudspeaker at the Pir Sultan mosque, the main one in Wana.
In the past two years, Pakistan has deployed 70,000 troops in the tribal areas for the first time since independence, and has staged five military operations.
Last month, Pakistan army troops using helicopter gunships and artillery raided several villages near Wana, capturing 25 people, none of whom was reported to be a top al Qaeda or Taliban figure.