According to a YouGov poll, Germans, Finns and Britons would support such an initiative in 62, 55 and 54 percent of cases, respectively.
Forty one percent of Swedes, as well as 39 percent of Frenchmen and 38 percent of Danes would support a controversial policy in their countries.
In Norway, only one-third of respondents would back the policy, the lowest figure among seven countries surveyed.
Europe is currently struggling with its largest migrant crisis since World War II. Refugees from the Middle East and North Africa are transiting to prosperous EU countries, including Germany and Sweden, via various routes including Italy, Greece, Turkey and the Balkan states.