Those in favor of EU membership climbed 2 percent compared to April, while those opposed dropped by the same amount.
The poll showed that just 53 percent of the country's electorate would vote at all in the referendum.
Voter apathy is lowest among citizens aged 50 and above, of whom 64 percent are determined to go to the polls. Potential turnout among those aged up to 35 is 54 percent.
According to the survey taken early in May before Estonia's victory in the Eurovision Song Contest, support for the country's entry into the EU has declined from 36 percent a month before to 35 percent, while the share of opponents has grown from 53 percent to 54 percent.
Emor analyst Aivar Voog said that statistically the change was not significant. "It seems that among Estonian optimists there are no highly reputed public opinion leaders who at the same time are not connected directly with the government," he said.
The Emor polls have shown that Estonian citizens normally accept specialists' opinions but do not believe officials, whether they work for the government or in EU institutions. This means, says Voog, that people who give any explanations must be well known and very competent, but at the same time seem independent.
The same problems are pointed out by Anu Toots, a political science professor at Tallinn Pedagogical University, who sees the reason for the rising Euroskepticism in the domestic and European policy of Prime Minister Mart Laar's Cabinet.
"Any requirements of the EU are served up in gloomy tones, which brings about a negative reaction. An overall mistrust of the government and officials at the same time spreads to the European Union. People have no trust in officials and no matter what they say about the EU it's counterproductive," Toots explained.
Toots said the public opinion campaign should be run like a political campaign.
The deputy chairman of the opposition Center Party, Peeter Kreitzberg, who supports the suspension of EU accession talks, told the Postimees daily in a comment on the poll results that the relationship between Euro-optimism and Euro-pessimism depends most on the government's activities.
"If the government carries on as it has until now and is unable or unwilling to explain its policy to the people and underestimates the people's understanding, then Euro-skepticism can only deepen," he said.
Hannes Rumm, manager of the state chancellery's EU information bureau, said the poll's outcome was expected, because the domestic policy crisis giving rise to alienation and social frustration is still smoldering.
The bureau's recent survey of attitudes toward the EU showed Estonia to be the most skeptical of the candidate countries and also the only one where opponents of the EU form the majority. In Latvia, for example, the percentage of Euro opponents is 33 and in Lithuania, 28. In Hungary Euroskeptics account for 15 percent and in Bulgaria only for 7 percent.