The findings of the poll also show that two thirds of respondents said EU action on migration was insufficient.
The Eurobarometer survey, published on Thursday, was conducted among 27,969 people from all EU countries on 9-18 April and was set up to be representative of the population as a whole. Across the EU, 74 per cent of respondents wanted the EU to do more on migration.
The EU has experienced an unprecedented influx of migrants over the last few years.
In March, MEPs adopted a report on the situation in the Mediterranean and the need for a holistic EU approach to migration.
The civil liberties committee approved on 30 May the European Commission's proposal to introduce a standard EU travel document for migrants. On 6 July, MEPs voted in favour of creating an EU border control system that will bring together the EU's border agency Frontex and national border management authorities.
The Commission is proposing an EU common list of safe countries to fast-track applications from people that come from countries that are considered safe. The plans have to be approved by Parliament and the Council before they can enter into force.
S&D group member Sylvie Guillaume, who is in charge of steering the proposal through Parliament, said: "The methodology for designating or reviewing a country as safe country of origin has been greatly improved."
The French MEP added, "A consultation process is now included to enable third parties, such as the European Asylum Support Office, UNHCR or NGOs to take part in the Commission's task of monitoring the EU common list."
Meanwhile, Turkish President Recep Tayyip Erdoğan's recent threat to reopen migrant routes from Turkey into Europe would mean a possible influx of as many as three million more migrants, according to reports.
In Turkey, there are some 2.8 million Syrian refugees alone, excluding the thousands of Afghans and Iraqis who are anxious to get into Europe. If Erdoğan carries out his threat to renege on Turkey's agreement with the EU, it is feared that as many as three million migrants will be looking to find new openings into Europe through the so-called Balkan route.
"The European Union is not acting sincerely with Turkey," he told French daily Le Monde. "We have taken in three million refugees, whereas the EU's only concern is keeping them out of its territory."
The Turkish President has been using the prospect of new waves of millions of migrants to pressure Brussels into accepting his demand that Turkish citizens be allowed to enter Europe freely without visas, which he sees as a first step toward eventual Turkish membership in the EU.
Elsewhere, the EU's demand that Ankara must overhaul its terror laws in return for visa-free travel is "impossible" in the aftermath of last month's attempted coup, Turkey's EU minister, Ömer Çelik, has warned.