The survey was conducted among 27,969 people representing all 28 member states and said to be representative of the population as a whole.
The fight against tax fraud was highlighted by respondents as the third most important priority for the EU. At EU level, 75 per cent of people wanted more action, compared to 69 per cent in Ireland and 70 per cent in the UK.
The fight for fair taxation in the EU became a priority for the Parliament long before the revelations of LuxLeaks and the Panama Papers.
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Since the start of the economic and financial crisis, MEPs have been pushing for greater transparency and an end to unfair tax practices.
Responding to the findings, Italian S&D group member Roberto Gualtieri, who chairs Parliament's economic and monetary affairs committee, said: "This shows that three quarters of the EU population expects more EU action on the fight against tax fraud: it is necessary to respond effectively to this concern."
He added, "The European Parliament is leading this fight, by adopting ambitious and concrete proposals to increase tax transparency and combat tax avoidance."
He said the assembly had also called for the automatic exchange of tax rulings between member states and public country-by-country reporting for multinationals, together with a common definition of tax havens and strong and concrete sanctions.
The MEP said, "We will continue to push member states to strengthen their tax policies, to close loopholes and to improve coordination at the EU and international level. It is only a matter of fairness towards EU citizens."
In the wake of the LuxLeaks scandal, MEPs set up two special committees on tax rulings. In its final report, which MEPs adopted in July 2016, the second special committee called for an EU register of beneficial owners of companies, a tax heavens blacklist and action against the misuse of patent box regimes.
The Panama Papers inquiry committee will start its work this autumn to assess how the European Commission and member states are fighting money laundering and tax evasion. This autumn MEPs will also start working on the public transparency rules for multinationals.
Meanwhile, according to a separate Eurobarometer survey, 71 per cent of Europeans want the EU to do more to protect its borders.
Parliament is working on a range of initiatives to beef up those controls and Latvian EPP group member Artis Pabriks, who is in charge of steering the plans through Parliament, said: "The European border and coast guard regulation will ensure that the EU external borders are safer and better managed."
The deputy added, "This is not a silver bullet that can solve the migration crisis that the EU is facing today or fully restore trust in the Schengen area, but it is very much needed first step."