American influence on the world stage is being sapped by widespread distrust of US intentions, not just in the Middle East and south Asia but also among traditional European allies, according to a survey of global opinions.

Suspicion of America outweighed faith in its good intentions by large margins in the Arab world and Pakistan, and even its heavyweight European ally Germany was more sceptical than trusting, a YouGov survey found. British and French opinion was more positive but still deeply divided.

Negative Arab and Pakistani perceptions of America as overweening and untrustworthy clearly pose a daunting foreign policy challenge for the Obama administration. The fact that 78% of Pakistanis questioned by YouGov said they did not trust America to act responsibly underlines Washington's serious lack of soft power in the region as it attempts to extricate itself from Afghanistan.

Attitudes towards the US in the Arab world were nearly as negative. Those respondents in the Middle East and north Africa who said they trusted America were outnumbered by more than two to one by those who said they did not, and 39% said they did not trust America at all.

The results suggest that Arab antipathy arising from the Iraq invasion and US support for Israel has not been softened by Obama's military withdrawal from Iraq, US support for the Arab spring and the relatively low-profile US role in the Libyan and Syrian conflicts.

Perhaps just as worrying for Washington is the lukewarm support among western European allies. More Germans questioned in the YouGov survey voiced misgivings than trust in the US. Perhaps surprisingly, in view of past wariness, French opinion was somewhat warmer: just over half of the French poll respondents trusted America, against 40% who did not.

The so-called special relationship between the US and Britain emerged from the survey as distinctly lopsided. There was widespread American affection for its close ally, but the sentiment was only partly requited, reflecting deep British ambivalence about America's powerful role in world affairs.

Two-thirds of Americans questioned by YouGov said they trusted Britain to act responsibly, with 15% dissenting. The leading traits Americans attributed to the UK were a respect for human rights and "a sensible voice in the world". More Americans than Britons thought the UK was "a force for good" on the world stage.

British perceptions seem to reflect the resentment of a junior partner in the relationship. Far more Britons than Americans saw the UK as a nation in decline, arguably showing a persistent deficit in national confidence even after the Olympics.

When asked to select a word they associated with America, a striking 40% of the British respondents chose "bullying", a greater proportion than in any other country or region covered by the survey. Only 12% thought the US was defined by its respect for human rights. Half of British respondents said they trusted America, and 41% said they did not.

There was a plurality in all the countries surveyed that foreign military intervention in Syria would make the situation there worse or have no impact. Opposition to such a move was most pronounced in Pakistan, and it was also prevalent in the Middle East and north Africa, where 40% of respondents said intervention would make matters worse, compared with 33% who said it would make things better. Six per cent said it would make no difference.

Among western countries, opposition to armed intervention was most entrenched in Britain, where the balance was 37% in favour and 21% against, with 12% saying it would have no impact. In the US, those for and against were more or less even (20% and 22%), but outnumbered by the 47% who said they simply did not know.

Sex, work and morality

French attitudes towards women who prioritise their careers over starting a family are a touch kinder than those in the Middle East, but a touch harsher than those in Pakistan, according to the polling.

Britons defended it as "a morally acceptable choice" by a 72%-6% margin, and Germans and Americans were also emphatic, but France was far more evenly divided: 30% deemed it acceptable to postpone parenthood in these circumstances, as against 27% who thought the reverse.

In Pakistan, by contrast, the support was by a more decisive 42%-27% margin. Only in the Middle East and north Africa did the suggestion run into more opposition than in France, with respondents rejecting it by a margin of 49% to 22%.

Elsewhere in the survey on questions of gender and sexual morality, opinion breaks down in more predictable ways, with liberalism prevailing in irreligious Europe, conservatism exerting more of a grip in the Muslim world, and the partially devout US occupying an intermediate position. On contraception, pornography and gay marriage the same pattern is found, as indeed it is on abortion, where France was by far the most pro-choice.

In one other respect, France was an outlier. A minority of the French said it was always wrong for a married man (49%) or indeed woman (44%) to have an affair, whereas the majority everywhere else that YouGov surveyed said it was always immoral.

YouGov polls Photograph: Graphic

Democracy v economy

The case for democracy is coming perilously close to being lost around the world, the poll reveals. In Pakistan and to a lesser extent across the Middle East and north Africa, respondents told YouGov that they thought a strong economy was more important than a system of government based on democracy. In Pakistan, the prioritising of growth over democracy was emphatic, by 71% to 22%. In a cross-border Middle Eastern sample of the online population – including Egypt, Tunisia and Libya – economic strength trumped democratic governance by 44% to 41%.

Perhaps more surprising is the nonchalant attitude towards democracy shown in some of the states that have enjoyed it for longest. Both France and the US were split down the middle on whether the economy or democracy should come first, with a 41%-41% divide in both nations. Britain's enthusiasm for its democracy was a little more emphatic: it was seen as the priority by 46%, against 38% who would put the economy first.

Only Germany was resolute in prioritising the political system. By 52% to 35%, German voters told YouGov that democracy had to come first.

• YouGov questioned 12,693 adults across the US, Britain, Europe, the Middle East and north Africa, Pakistan and China between 10-25 August 2012. Data was weighted to be nationally representative of adult populations in Britain, US, France, Germany and the US; elsewhere it was representative of the online population.