WASHINGTON (Reuters) — If US 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 US 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 US," said Sally McNamara, a European affairs expert at the conservative Heritage Foundation in Washington. Accustomed to being at the centre of US 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 anaemic economy.

It will not be lost on his European hosts that Obama, who visited Europe six times in his first year, is dashing to Lisbon for little more than 24 hours on the ground after conducting a ten-day four-country tour of Asia. The White House insists that Obama's engagement with economically dynamic Asia will not come at the expense of America's "enduring partnership" with less-vibrant Europe. But analysts believe sweeping Republican gains in the November 2 midterm elections, which could cause legislative gridlock, will make it harder for him to make progress on top European concerns like financial regulation, climate change and trade.

Obama may also have to deal with fallout from last week's Group of 20 summit in Seoul, where he faced a backlash over US monetary easing policy, resistance to his push for hard targets on global balanced growth and reluctance to join in pressuring China over its currency. Reflecting a growing estrangement over economic policy, German Chancellor Angela Merkel and British Prime Minister David Cameron have strongly opposed Obama's call for stimulating economic expansion with more government spending. They prefer to stress fiscal discipline.

German Finance Minister Wolfgang Schaeuble took the rhetoric to a new level earlier this month when he said the Federal Reserve's decision to pump $600 billion into the US economy was "clueless." Germany, China and other big exporters see it as a backdoor way to cheapen the dollar and give US goods a trade advantage. Meeting first with Nato leaders and then with heads of the 27-nation EU, the world's biggest economic bloc, Obama will undoubtedly seek to ease tensions. Topping the Nato agenda will be Afghanistan. Obama wants allies to commit to a blueprint for shifting primary security responsibility to Afghan forces by 2014. He is mindful of NATO's need for an exit strategy in the increasingly unpopular war but hopes to avoid a disorderly rush for the door.

How well he fares could be a sign of how much sway he still holds with Europe. Though Obama remains popular among ordinary Europeans, their leaders are no longer starry-eyed about him. Many welcome his more multilateral approach after what critics derided as "cowboy diplomacy" under George W. Bush. But there is also disappointment in Europe that Obama has not done more to advance the fight against climate change or meet his promise to close the military prison at Guantánamo.

Nearly two years after he took office, traditional European powers have also seen their international clout heavily diluted with his push to elevate the G20 over the G8 as the main forum for coordinating global economic policy. "It's a touchy issue," said Charles Kupchan, an expert on international relations at Georgetown University. "On Obama's watch, there has been a demotion of Europe's voice."

The EU summit was originally scheduled for May in Madrid, but it was called off after Obama decided not to go. US officials said it would have been little more than a photo-op.

Then the euro zone debt crisis erupted, with the near-collapse of Greece's sovereign debt market and a spillover effect on US financial markets and the economy. That sent officials scrambling to reschedule the summit, which now is sure to discuss Ireland's emerging debt woes. Obama said last week at the G20 that he had developed "genuine friendship" with some foreign leaders, including Merkel. But European diplomats demurred, saying he had mostly forged working relationships, not close personal bonds.

Born in Hawaii and raised partly in Indonesia, Obama — who lacks the instinctive European focus of his predecessors — has declared he wants to be America's first "Pacific president". Europeans may be wondering where that leaves the Atlantic.