The US military said heavy fighting in central Afghanistan killed 13 people on Monday, including a second US soldier in two days.
The latest blow to US forces, already suffering their bloodiest year in Afghanistan since ousting the Taliban from power in 2001, came when a US patrol was attacked by small arms, rocket-propelled grenades and mortars in a village in Uruzgan province.
A US statement said an Afghan soldier was also killed, along with 11 suspects, while three US troops and an Afghan soldier were wounded in the heavy fighting west of Deh Rawud.
It said initial reports indicated eight fighters were captured from a group of 15-30 attackers.
In an earlier incident in the capital, Kabul, three Afghan police officers were critically wounded when a bomb exploded at their post on a road leading to the airport.
Another US soldier was killed and one hurt in the southern province of Helmand on Sunday, while six US troops were in stable condition after their convoy was hit by a roadside bomb that day in Kunar province, the military said.
The latest casualties brought US combat deaths in Afghanistan this year to 37.
The fresh violence came after a message was delivered by Omar via field radio to the Taliban's leadership council, a Taliban spokesman said.
"Unite, and do not disagree, continue your jihad (holy war) and victory will be yours," said a recording of the message, purporting to come from Omar, handed to Reuters in the southern city of Kandahar on Monday by a man who did not identify himself.
"Unite, and do not disagree, continue your jihad (holy war) and victory will be yours"
Mullah Mohammad Omar, Taliban leader
Omar's whereabouts have remained unknown since US-led forces overthrew the Taliban for refusing to hand over Osama bin Laden and other al-Qaida leaders responsible for the 11 September attacks on US cities in 2001.