Only three other political parties in Sweden registered a higher level of support, according to the poll.
Support for the Green Party, Sweden's third largest party, edged up 0.3 percent to 9.3 percent.
1,000 Swedes participated in the survey, answering the question "Which political party do you like best in national politics?"
The currently governing centre-right Alliance, consisting of the Moderate Party, the Christian Democrats, the Centre Party and the Liberal Party (Folkpartiet), still maintains a combined edge over the centre-left opposition consisting of the Social Democrats, the Green Party and the Left Party.
"But none of the blocks would get their own majority in the Riksdag if there was an election today, and the lead for the centre-right is only 2.8 percentage units," Skop analyst Birgitta Hultåker said in a statement.
The Left Party's support decreased by 1.8 percentage units in the latest poll, receiving only 4.3 percent of the vote.
"If it wasn't for the Left Party's decline, the opposition would be in the majority," says Hultåker.
After a slump in February and March, the new figures represent the third consecutive poll Skop showing growing numbers for the Sweden Democrats.
The Moderate Party: 33,4 percent, +/-0
The Liberal Party (Folkpartiet): 5,4 percent, -0,6
The Centre Party: 5,5 percent, +1,2
The Christian Democrats: 3,8 percent, -0,2
The Social Democrats: 31,7 percent, +1,3
The Left Party: 4,3 percent, -1,8
The Green Party: 9,3 percent, +0,3
The Sweden Democrats: 6,5 percent, +0,6