Published by the daily Dagens Nyheter (DN), the Ipsos poll confirmed the Sweden Democrats' soaring popularity in recent months and the decline in support for the leading Social Democrats, which has lost one-fourth of its voters since the 2014 election.
With 20 percent in support, according to Ipsos, the far-right group is gaining on the conservative Moderates (22 percent) and is now only four points behind Prime Minister Stefan Löfven's Social Democrats (24 percent).
The poll suggests the Sweden Democrats are most popular among men (26 percent). Some are former Social Democrats voters attracted to the group's anti-immigration rhetoric.
The Nordic nation has registered some 400,000 asylum applications since 2012, one for every 25 inhabitants.
To contain the refugee influx, the minority centre-left government has reestablished border controls and toughened conditions for granting asylum, residence permits and family reunification.
- How to understand the 2018 Swedish election through Abba songs
- How to vote in Sweden's 2018 election
But some analysts warn the measures might not be enough for the government to win over voters.
“The Social Democrats have voters who are drawn to opposite sides. There are the traditional workers in smaller areas and the urban voters who appreciate cultural diversity,” David Ahlin, who is responsible for the Ipsos poll, told Dagens Nyheter.
However, Ahlin said the Social Democrats' “success in keeping a wide coalition of voters together doesn't seem to be working any longer”.
Altogether, Sweden's leftist parties have 37 percent in support, behind a centre-right alliance on 39 percent, according to the survey which interviewed 1,818 people through telephone and online.