The survey, conducted by the European Council on Foreign Relations (ECFR), a pan-European think-tank, also found that there is now significant support for investing in European-level defence.
The survey findings come in the wake of US President Joe Biden's participation in last week's EU summit in which both the US and EU pledged to reignite the transatlantic relationship.
The last US president to attend a meeting of EU leaders was Barack Obama in 2009 when he attended a summit in Prague.
The survey showed that at least 60 percent of respondents in every country polled - and 67 percent across all the countries - felt their country could not depend on US support in the event of a major crisis.
Two thirds of those surveyed indicated the importance of Europe looking after its own defence capabilities rather than relying primarily on the US, with this backing most pronounced in Portugal (72 percent), Sweden (71 percent), Spain (71 percent), France (70 percent) and Poland (69 percent). Interestingly, 74 percent of British respondents also shared this view.
The survey also said there is “deep ambivalence” towards the United States in the event of conflict with China or Russia - with many Europeans keen to be neutral in such a scenario.
There is, said the authors of the survey, also a strong sense among Europeans that China will overtake the US as the world’s leading superpower within the next decade.
“There is a strong sense among Europeans that China will overtake the US as the world’s leading superpower within the next decade”
Meanwhile, both the EU and US have been urged to insist that China lifts its sanctions against five MEPs before it considers signing off on a multi-million-euro trade deal.
The Greens in Parliament have appealed to both sides to tell China that ratification of the EU-China Investment Agreement will not be considered until the Chinese Communist Party lifts sanctions imposed last week on five MEPs and several EU bodies, including Parliament’s human rights sub-committee.
China has since imposed similar sanctions on senior political figures in the UK, including former Conservative party leader Iain Duncan Smith.
German Greens/EFA member Reinhard Bütikofer is one of the five cross-party MEPs targeted and Greens co-leader Philippe Lamberts said, “We stand with Bütikofer and all those targeted by the Chinese Communist Party for standing up for democratic values.”
The Belgian member said he “strongly condemned the attacks against our colleagues and fellow citizens by the Chinese government.”
Lamberts added, “It is obvious that there can be no question of even taking into consideration the ratification of the EU-China Investment Agreement until the Chinese Communist Party lifts the sanctions.”