Figures for approval of the EU are virtually back at their pre-crisis levels in 2007, it says.
The survey, commissioned by the Parliament and published on Friday, shows that EU membership is a "good thing" in the eyes of 57 per cent of Europeans.
This is up by four percentage points compared to the previous survey of September last year and almost at the same level as in 2007 (58 per cent), before the financial and economic crisis set in. Percentages vary significantly, however, from country to country.
Reacting to the findings, European Parliament President Antonio Tajani said, "The findings of the European Parliament survey of Europeans' attitudes towards the European Union are, for the first time since the start of the crisis in 2007, very encouraging.
"They show that European citizens expect the Union to respond with a single voice to their very acute fears about recent international upheavals that have made the world more uncertain and dangerous. It is up to us, as political leaders, to show them that they are right."
Reacting to the latest geopolitical events, such as the growing instability in the Arab world, the increasing influence of Russia and China, Brexit and the election of Donald Trump, up to 73 per cent of respondents prefer the EU to find a common response over individual national actions.
A strong majority also calls for the EU to do more in addressing current challenges, such as the fight against terrorism (80 per cent) and unemployment (78 per cent), protecting the environment (75 per cent) and tackling tax fraud (74 per cent).
An increasing number of Europeans (43 per cent) feel that their voices count at EU level, more than at any other time since 2007 and up by six points compared to 2016. By contrast, six Europeans in 10 consider that their voice counts in their country, which is 10 points more than in 2016.
The survey said that the overwhelming majority of Europeans say that inequalities between social classes are significant and a third of them doubt that the crisis will be over for many years.