Nato leaders at a summit are continuing to limit troop deployment to south Afghanistan, despite calls from the US to accept "difficult assignments".
Canada has had dozens of troops killed in Afghanistan
France and Germany have agreed to small changes on how troops can be used, but will not move large numbers to the area where Nato faces a resurgent Taleban.
But the Dutch and Romanians are among those agreeing to relax such curbs.
The US, UK, Canada and the Netherlands have borne the brunt of fierce fighting with the militants in the south.
Violence has risen to heights not seen since the toppling of the Taleban.
Some 4,000 people are believed to have died this year in the insurgency - about a quarter of them civilians.
In fresh violence, two Nato soldiers were killed when their vehicle struck a roadside bomb in Logar province on Tuesday. The nationalities of the victims have not yet been disclosed.
Details of the agreement to relax restrictions are due to be announced shortly.
Nato's secretary general wants more troops for Afghanistan
Correspondents say the combat curbs have been the most contentious issue at the two-day summit in Latvia, following tension over the reluctance of France, Germany, Spain and Italy to send their troops to southern Afghanistan.
Nato sources say more than three-quarters of the 32,000-strong force in Afghanistan will soon be allowed to operate more widely if necessary.
Those agreeing to ease the restrictions on deployment against the Taleban include the Dutch, Romanians and smaller nations such as Slovenia and Luxembourg.
France, Germany, Spain and Italy have said they will now send help to trouble zones outside their areas, but only in emergencies.
"This has been our clear position from the beginning," Italian Prime Minister Romano Prodi told journalists after a working dinner on the issue.
"That also goes for the French president, the German chancellor and the Spanish."
An alliance spokesman told Reuters news agency that three countries had also agreed to send more troops, with several more agreeing to increase funding for Afghanistan.
Commanders have requested 2,500 extra troops for the battle in the south of the country.
Earlier, US President George W Bush called on Nato not to undermine the effort in Afghanistan.
"For Nato to succeed, its commanders must have the resources and flexibility they need to do their jobs," he said.
Nato Secretary General Jaap de Hoop Scheffer described the Afghan operation - Nato's first outside Europe - as "mission possible", and said that it might even be able to start pulling out from 2008.
The summit, the first Nato meeting in an ex-Soviet state, will conclude after discussions about Nato's role in the 21st Century.
The alliance leaders will also discuss ways to enhance Nato's partnership activities, including efforts to draw countries like Japan and Australia more closely into alliance activities.
Speaking in Latvia, Mr Bush said Nato would keep its doors open to new members, including Georgia and Ukraine.
The US president said the US would support Georgia's bid to join Nato as long as it continued on the path of reform and that membership of the military bloc would be open to Ukraine if the people chose it.
Correspondents say membership for either country could further strain their relations with Moscow.
MAIN FLASHPOINTS IN AFGHANISTAN
There are 32,500 Nato-led troops in Afghanistan
Main troop contributors: US, (11,800), UK (6,000), Germany (2,700) Canada, (2,500) Netherlands (2,000), Italy, (1,800) and France (975)