The world's love affair with Barack Obama is not quite over – but it's on the rocks. A survey of global opinion of the US president shows large numbers of non-Americans feel badly let down by the man awarded the 2009 Nobel peace prize.

A Pew Research Centre poll of attitudes toward the US in 21 countries found that confidence in Obama's foreign policy has fallen sharply since he took office three years ago, particularly over the use of drone attacks. Hopes that Washington would prove more internationalist, seek UN approval for military action and be more even-handed in the Israeli-Palestinian conflict have been dashed. Foreigners also feel let down by the president's inertia on climate change.

Perhaps most worryingly for Washington, the real collapse in confidence is over the US economy, with majorities in the UK, Germany and France saying that China is now the world's top economic power. But Obama still commands far more respect than his predecessor, George Bush, and most Europeans hope he is re-elected.

The poll reveals particular hostility to US drone attacks in Pakistan, Afghanistan and Yemen. Although Washington claims the attacks are carefully targeted at major terrorists, they frequently kill civilians.

The drone strikes are backed by 62% of Americans but have only minority support in every other country polled by Pew. The strongest overseas support for the US strategy is in Britain, where 44% approve and 47% are against. But in France, China, Mexico and Russia there are large majorities opposed to it.

The US president's standing remains strong in Europe, where he has an 80% approval rating – down just 6% on three years ago. But it is a different story elsewhere. The sharpest drop in confidence in Obama has been in China, where support has fallen from 62% in 2009 to just 38% this year.

He commands similar backing in Russia.

Perhaps unsurprisingly, Obama's lowest standing is in the Muslim world, where fewer than one in four approve of his policies. That is still markedly higher than views of the US as a whole. Just 15% of people in Muslim countries have a favourable view of the US.

The poll shows foreigners feel let down by Obama on a range of policies. When he came to power, nearly half of non-Americans thought the new US president would seek international approval for the to use of military force. Just 29% believe he has fulfilled that hope. He was also expected to "be fair with the Israelis and Palestinians" and to confront climate change. Large majorities feel let down on those issues.

Still, the romance many Europeans developed with Obama, giving them a more sentimental view of the president than most Americans have, largely continued. Large majorities in Europe would like to see him re-elected, led by 92% of those polled in France.

This is not so in the Middle East, where three out of four Egyptians and clear majorities in other countries want him out of office.

The economic standing of the US has fallen sharply, too. Four years ago, 44% of Britons regarded the US as the world's major economic power; just 28% said China. Today those positions are reversed, with 58% saying it is China and 29% the US. Opinion in Germany, France and Spain was similar.