Nearly two thirds think decisions on migration should be taken at the EU level rather than nationally, but the answers vary considerably from country to country. In many questions, Croatia follows the European average.
The public opinion survey covered 28,150 EU citizens older than 15 and was conducted on September 19-29, when the arrival of migrants on the EU's borders and their tragic deaths received extensive media coverage.
Two-thirds of all Europeans (66%) believe more decisions on migration should be taken at the European level. Opinion ranged from 79-81% in the Netherlands, Luxembourg, Spain, Germany and Cyprus to 40% in Estonia, Poland and Slovakia.
Sixty-two percent of Croatians believe migration problems should be dealt with at the European level and 61% welcome a decision to allocate funds to the member states which are hardest hit by the migration wave. The European average is 62%.
By a wide majority of 78%, Europeans agree that asylum seekers should be better distributed among all EU states. The same opinion is shared by 92-97% of respondents in Malta, Sweden and Germany, but, at the other end of the scale, only 31-33% in Slovakia and the Czech Republic.
Of those 78%, 75% agree the distribution of asylum seekers should be decided at EU level on the basis of binding quotas.
As many as 89% of Croatians, just after Cypriots and Germans, support the quota system, which is 14% above the EU average.
According to this survey, as the refugee crisis was intensifying, 47% of respondents said immigration was the biggest challenge facing the EU - up from 14% in 2013.
Terrorism is the biggest EU concern for 26% of the respondents, up from 11% in 2013. However, according to 61% of Croatians, the EU's biggest problem is unemployment, up from the European average of 49%.
Croatian, French and Portuguese respondents consider migration a minor EU problem, with only 28% of Croatians seeing immigration as the EU's biggest challenge, the European average being 47%.