The Public Issue poll was published in the Kathimerini newspaper Sunday as the coast guard searched the sea off Corfu for 22 Afghan migrants missing after the Dutch-flagged wooden trawler transporting them and scores of their countrymen sank. The search went on Monday.
Authorities believe two of the 241 people rescued are Turkish human smugglers who were trying to take the migrants from Greece to Italy.
The poll of 523 Greeks found that 39 percent "definitely agreed" with the fence plan. Another 20 percent said they "probably agreed" and only 21 percent "definitely disagreed."
The proposal set off dueling rallies in Athens Saturday. In the Aghios Panteleimonas neighborhood, 300 people, including members of the far-right Chryssi Avgi group, protested the presence of immigrants in Greece. They fought with police who kept them from confronting participants from a rally in central Athens to defend migrants and oppose the fence. Police said 13 people, mostly right-wing extremists, were arrested.