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(Reuters) - If President Barack Obama is not yet convinced that his international star power has faded, his next round of transatlantic summitry should clear up any lingering doubts.

Coming off a marathon Asia trip where Obama often found himself rebuffed by fellow world leaders, he will head to Europe this week where the agenda will be clouded by a growing divide over economic strategy and a sense of neglect among traditional U.S. allies.

His challenge is to reassure European partners that, despite political weakness at home and embarrassing setbacks abroad, he remains committed to better cooperation on issues ranging from the war in Afghanistan to the fight against trade protectionism.

But it will not be easy for Obama, whose Democratic Party suffered heavy losses in this month's congressional elections, to dispel the impression that his stature has been diminished on the world stage. He will attend back-to-back NATO and European Union summits in Lisbon on Friday and Saturday.

"The tricky thing for Obama is to show the Europeans not only that he's still important to them but that they're still important to the U.S.," said Sally McNamara, a European affairs expert at the conservative Heritage Foundation in Washington.

Accustomed to being at the center of U.S. foreign policy, Europe may be feeling jilted.

Despite the European love affair with Obama when he was elected two years ago, he has let transatlantic ties slip down his priorities list while focusing on rising Asian powers like China and India and domestic concerns such as high unemployment and an anemic economy.