Rasmussen 56, who took over on Saturday as secretary-general of the North Atlantic Treaty Organisation, faces many challenges but none more daunting than finding a winning strategy for the war in Afghanistan and improving relations with its former Cold War foe Russia.
The former Danish prime minister also has the delicate task of managing expectations in Ukraine and Georgia, former Soviet republics that have been promised eventual NATO membership despite Moscow's resistance.
Rasmussen said the 28-member alliance and Russia had common goals in the key areas of counter-terrorism, Afghanistan, disarmament and non-proliferation.
The situation in Afghanistan will require a comprehensive approach involving both military and civilian efforts to stabilise the country, he said in an interview with Reuters.
He has to persuade reluctant European allies to commit more troops, money and other resources to Afghanistan, where opinion polls have shown popular support for the war waning in Europe as casualties increase among NATO forces.
"First of all we have to make sure that the security situation improves, but obviously there's no military solution solely," Rasmussen said.
"We need to reinforce the interaction between our military efforts and civilian reconstruction. So the comprehensive approach will be one of my focal areas," he said.
On relations with Russia, "I think we should develop practical cooperation ... while of course insisting on Russian compliance with her international obligations including respect of the sovereignty and integrity of her neighbours," Rasmussen said.
NATO's relations with Russia were damaged by the five-day Russia-Georgia war last year.
Rasmussen will try to repair this damage, mindful also of the need to cooperate with Russia on global security issues.
The alliance has put the subject of Georgian and Ukrainian NATO membership on the back burner in the interest of getting relations with Moscow back on track, but says membership remains open to countries that meet NATO standards.
"My goal is to develop a true strategic partnership with Russia, while of course realising that there might be differences in our positions in a number of areas," Rasmussen said.
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