But whether Anders Fogh Rasmussen can persuade NATO countries to commit more resources to a war that is becoming more deadly on the ground and less popular at home remains to be seen.
Rasmussen's choice of Afghanistan for his maiden voyage was clearly meant to put an exclamation point on his declaration that the conflict there is the North Atlantic Treaty Organization's most important operation, a must-win if the alliance is to remain relevant to global security.
"That starts with succeeding in Afghanistan," the former Danish prime minister told reporters after taking office as NATO's secretary-general Monday.
NATO must "help prevent Afghanistan from becoming again the Grand Central Station of international terrorism," he said. "The moral argument is also powerful: Anyone who believes in basic human rights, including women's rights, should support this mission."
Such support, though, is in dwindling supply throughout much of Europe.
After the deadliest month for Western troops in Afghanistan since the U.S.-led invasion nearly eight years ago, public opposition to the war has intensified on this side of the Atlantic.
That has been especially true here in Britain, America's staunchest ally, which suffered the loss of eight troops within a 24-hour period. Public and parliamentary outcries have erupted over whether British troops are adequately equipped. News that the head of the British army had to ride in an American helicopter on a recent visit because British choppers were unavailable only fueled the anger.
Afghan civilians also are being felled by violence. On Wednesday, the U.S. military said it was investigating allegations that three children and a man were killed by allied military action outside Kandahar in southern Afghanistan.
The rising death toll, which has put 2009 on track to be the deadliest year of the war for Western troops, has aggravated Rasmussen's task of keeping NATO members committed to the war, let alone persuading them to send more troops, as the Obama administration has lobbied for.
"That's not going to be forthcoming," Lisa Aronsson, an analyst at the Royal United Services Institute, a London-based security think tank, said bluntly.
"The casualty rate in July is really hitting home for Europeans. They're already financially strapped; they're already giving what they can.
"If Obama couldn't do it, considering the political capital he had at the beginning of the year, it's going to be difficult" for Rasmussen, Aronsson said.
His immediate predecessor as NATO secretary-general, Jaap de Hoop Scheffer of the Netherlands, likewise called Afghanistan the alliance's No. 1 priority and repeatedly urged member nations to ramp up their resources there. But he left office frustrated on that score, and little suggests that Rasmussen, despite his diplomatic contacts and higher profile as a former head of government, will have any more success.
Of the 64,000 foreign troops in Afghanistan, about half are from the United States and most of the rest from other NATO countries. The Americans, British, Canadians and Dutch have seen the most fighting.
The reluctance of some heavyweight European nations such as Germany to send more soldiers and allow them a more active combat role is a particularly bitter irony for Obama. His popularity in this region was built in large part on his stance against the "bad war" in Iraq, yet now the "good war" in Afghanistan is increasingly turning into a poisoned chalice as well.
To buoy support, Rasmussen has emphasized that the battle against Al Qaeda and Islamic terrorism is as crucial to Europe's security as it is to America's. Many Europeans have yet to be convinced of that, despite successful terrorist attacks on the London and Madrid transit systems and reports of thwarted attacks elsewhere.
Perhaps in a nod to hard political realities, Rasmussen may be shifting toward highlighting the need for civilian expertise in rebuilding Afghanistan, given that military reinforcements from Europe are unlikely, Aronsson said.
"Afghanistan needs more trainers; it means more civilian support, and more help for the Afghans to build their institutions," Rasmussen said at his news conference Monday. "NATO -- by which I mean both sides of the Atlantic -- will do its full part, but we can't do it alone. This has to be an international team effort."
But he added: "Let no Taliban propagandist try to sell my message as a run for the exit. It is not. We will support the Afghan people for as long as it takes. Let me repeat that: for as long as it takes."