A statement by the US military said two soldiers had died in fighting near the Pakistan border in Paktika on Monday.
A third was killed on the same day in a separate incident in neighbouring Paktia province while on patrol, it said.
Paktia and Paktika are both heartlands for Taliban fighters opposing what it says is the US-appointed government of interim President Hamid Karzai.
US toll rising
In addition to the three deaths, 14 US soldiers had been wounded in eight separate incidents on Monday, said a spokesman for the US-led force in Afghanistan, Major Scott Nelson.
At least nine fighters were killed, he added.
"As operations continue, resistance is expected," he said, adding that six Afghan National Army soldiers were wounded and one was reported missing.
More than 17,000 US troops and their allies are fighting remnants of the Taliban, overthrown in 2001 by a US-led invasion.
Residents say they are being
coerced to register
Karzai - in New York to attend the United Nations General Assembly - is expected to defeat 17 opponents standing against him in elections due to take place on 9 October.
Abd al-Wahid from southern Afghanistan's Zabul province, told Aljazeera.net that residents have never felt so insecure and so much distrust.
They are being harassed by both government officials and Taliban supporters, he said.
Some residents have been threatened with the withholding of medical facilities, food aid and security if they do not register for what Afghans call a "Karzai card" (voter card).