Answering questions from an audience at the Atlantic Council, a public policy group, he added: "We should expand our training mission. I consider it easier for European countries to contribute to our training mission with personnel as well as with finances, than with combat troops."
His comments came on the same day that European defence ministers, meeting informally in Sweden, expressed reluctance to send a significant number of reinforcements.
Soren Gade, the Danish defence minister, said "if you look at Europe, I don't hear any voices saying we have an additional five or ten thousand soldiers to send to Afghanistan".
Rasmussen, who took over Nato's top job last month, said he agreed with the grim assessment of the war by the top US and Nato commander in Afghanistan, General Stanley McChrystal, but stopped short of calling for more troops himself.
"Basically I share the views presented by General McChrystal," Rasmussen said when asked about a leaked report by the commander.
The general's analysis recognises there is no military solution to the war and calls for a "more comprehensive approach" that seeks to safeguard the population, Rasmussen said.
But Rasmussen said he was not ready to comment on McChrystal's request for tens of thousands of additional troops to reinforce efforts to counter Taliban fighters, saying it would be "premature".
"Now we have to go through his initial assessment and analysis, discuss it within the alliance, agree on the approach and then we can make a decision on resources," he said.
The McChrystal assessment described daunting challenges in Afghanistan, with a government plagued by corruption and the Taliban extending its reach.
|McChrystal's report said Nato troops often lacked basic understanding of Afghans [AFP]
Rasmussen agreed that the Afghan government had to be held accountable by donors to fight corruption and deliver services to its people, calling for a new "compact" between outside governments and Kabul.
But McChrystal's leaked assessment included withering criticism of Nato's International Security Assistance Force, saying that troops often lacked basic understanding of Afghan society.
Rasmussen said he was aware of frustrations in Washington, including restrictions some Nato nations put on their forces and delays in Nato decision-making, but added that he was "already working hard to address those very real problems".
But he criticised those in the US who belittle the contributions of allies, pointing to 9,000 additional non-US troops who have joined the Afghan fight in the past 18 months.
"The allies are not running from the fight, despite the conventional wisdom," he said.
Such US criticism was counterproductive, unjustified and risked leaving allies "less inclined to make those efforts and those sacrifices" in the future, he added.
"Talking down the European and Canadian contributions – as some in the United States do on occasion - can become a self-fulfilling prophesy."
The Netherlands and Canada have already set 2010 and 2011 withdrawal timelines but Rasmussen pledged that Nato "will stay for as long as it takes to succeed".
"None of this will be quick and none of it will be easy," he said. "We will need to have patience. We will need more resources. And, unfortunately, we will lose more young soldiers to the terrorist attacks of the Taliban."
Rasmussen's visit to Washington comes at a crucial juncture as the administration of Barack Obama, the US president, debates war strategy and a request from McChrystal for up to 40,000 additional troops.
Rasmussen held talks on Monday with Robert Gates, the US defence secretary, and was due to meet Obama on Tuesday.
Obama has said he will not decide on further reinforcements for Afghanistan until after a broad review of strategy.
The Pentagon said on Monday even if Obama approved additional deployments immediately, that would not happen until at least next year.
"There is a certain amount of train-up that is required to prepare ... there is a certain amount of logistics in terms of moving equipment," Bryan Whitman, a Pentagon spokesman, said.