Three soldiers with US-led multinational forces were killed in a clash in the eastern province of Kunar.
A soldier with Nato forces was killed along with an Afghan soldier in a gun battle with Taliban fighters in the southern province of Uruzgan. Three other Nato soldiers were wounded in the Uruzgan incident, a spokesman for the force said.
Sergeant Chris Miller, a multinational force spokesman, told Reuters: "We know that three coalition soldiers were killed today in action in Kunar."
A statement said: "[A] patrol was attacked with small-arms fire. The patrol returned fire with small arms, artillery and close air support.
"The patrol continued to exchange fire and repelled about 100 to 150 insurgents for nearly four hours. Insurgent casualties have yet to be reported."
Separately, the Nato-led force said a US soldier embedded with the Afghan army and an Afghan soldier were killed on Saturday in heavy fighting with Taliban insurgents in southern Afghanistan.
The soldiers came into contact with "a large Taliban force" in Uruzgan province and were killed in an ensuing gun battle, an International Security Assistance Force (ISAF) spokesman told AFP in Kandahar.
Three other US soldiers were wounded, ISAF said in a statement later.
ISAF initially reported that the four foreign soldiers were with the Nato force but said later they were US soldiers who were embedded with the Afghan army as trainers and "operating in support of the ISAF mission".
The US-led multinational force later confirmed they were serving with the force.
Saturday's toll brings the number of foreign soldiers killed to 92 since the start of the year.
The clashes are part of daily violence, but they coincided with the release of a message that the Taliban said was from their elusive leader, Mullah Mohammad Omar.
The message from Omar, who has called on Afghans to support the Taliban in their war to drive out foreign forces from the country, came on the 87th anniversary of Afghanistan's independence from Britain.
Afghanistan celebrated the 87th
anniversary of its independence
It was read to Reuters over a satellite phone by a Taliban spokesman, Mohammad Hanif.
"Celebrating Afghan Independence Day would amount to self-deception at a time when the infidel forces of the entire world have occupied the country," the message said.
"It is madness to celebrate Independence Day or to raise the national flag when the country is occupied. Rise against the infidel forces and help Taliban in the Jihad (holy war) to free Afghanistan from the slavery of the occupiers."
The whereabouts of the one-eyed Omar are not known. Afghan officials say he is hiding somewhere in neighbouring Pakistan.
The Taliban and their allies, such as the al-Qaeda network of Osama bin Laden, are mostly active in southern and eastern parts of the country close to the border with Pakistan.
Most of the violence has been concentrated in southern areas, where Nato last month assumed security responsibility from multinational forces.
The move is the biggest ground operation by the alliance in its history and is aimed at allowing the US military to cut down the size of its force in Afghanistan.
Nato is expected to expand its mission into the east later this year too.