However, the three opposition parties still lead the government by 10 percent in the ratings.
In the latest research, 41.9 percent of voters backed the Social Democrats, a fall of 3.1 percent in the last month. The Left Party has surged 1.5 percent to 5.9 percent.
Other changes in the levels of party support were minor. The Christian Democrats increased slightly to 4.8 percent but are still hovering uncomfortably close to the 4% limit for presence in parliament.
The Moderates rose by 1 percent to 24.8 percent. In total, the Alliance block is backed by 42.4 percent of voters while the opposition enjoys 52.4 percent support, according to the results published in Dagens Nyheter.
The poll was carried out between June 7th and June 20th and 2,206 people were interviewed.