The four-party opposition alliance, headed by the leader of the conservative Moderate Party Fredrik Reinfeldt, would garner 48.1 percent of voter sympathies, the Sifo survey in daily Svenska Dagbladet showed.
The Social Democrats and their allies, the Left party and the Greens, were credited with 47.4 percent of voting intentions.
Saturday’s poll gave the alliance a narrower lead than a series of surveys taken during August.
Support for the Social Democrats stood at 34.2 percent, down 1.6 percentage points from Sifo’s previous survey, published on August 26, while support for the largest centre-right party, the Moderates, was down 0.4 percentage points at 23.9 percent.
The survey showed the proportion of those saying they were undecided about which party to vote for, or who would cast a blank vote stood at 13.1 percent.
Swedes are due to go to the polls on September 17th.
The Social Democrats have governed the country for the better part of the post-war period with only a few brief interruptions, but political observers have suggested that Persson, who has served as prime minister since 1996, has outstayed his welcome among voters who feel the time has come for a change.
Meanwhile, the opposition alliance – consisting of the Moderates, the Liberals, the Centrists and the Christian Democrats and known for being notoriously divided – has presented an unusually united front.
Sifo interviewed 1,241 people between August 28th and 31st.