President Barack Obama remains popular around the world, amid declining job approval ratings at home, a survey by the Pew Research Center suggests.
Trust in Mr Obama has declined since 2009, but remains much higher than for President George W Bush, Pew says.
Muslim countries including Egypt and Pakistan continue to view both the US and Mr Obama unfavourably.
Nato allies favour removing troops from Afghanistan but back US counter-terrorism policies, the study suggests.
'Do the right thing'
In the UK, a plurality of those surveyed (49%) favour keeping troops in Afghanistan.
A majority in France (52%) and Germany (58%) would prefer to pull troops out, but the overall perception of the US in both countries, as in the UK, remains highly positive.
More than 80% of those polled in all three countries also expressed confidence that Mr Obama would "do the right thing" in world affairs.
In Kenya, a striking 95% of respondents said they believed he would to the right thing. In Nigeria the figure was 84%, and it exceeded 70% in India, Japan and South Korea.
People in Muslim countries surveyed continue to perceive the US as a military threat, and their opposition to US foreign polices remains strong.
In Egypt, where Mr Obama gave a landmark address to the Muslim world in 2009, favourable attitudes towards the US have dropped 10 percentage points to 17%.
Pew surveyed 22 countries across the globe for its report. Other key findings include:
- Arizona's new immigration law has hurt America's standing in Mexico, where favourable attitudes towards the US have tumbled 18 percentage points since the law was passed.
- An increasing number of people view China as the world's leading economic power - the number of people who see the US as dominant is higher, but falling year by year. China's economic ascendence is viewed positively in Pakistan, India and Japan, while it is of concern in continental Europe and the US.
- Pakistan is the only country surveyed to voice support for a nuclear-armed Iran. Majorities in 10 countries - including Jordan, Egypt and Brazil - would consider military action to prevent Iran from acquiring nuclear weapons.
- No Muslim country surveyed recorded majority support for suicide bombing, al-Qaeda or Osama Bin Laden.
- German Chancellor Angela Merkel gets higher marks on international affairs in France than in Germany, while Germans view French President Nicolas Sarkozy more favourably than the French do.