The new figures are the Social Democrats' worst since February 2012, after Löfven took over the party from former leader Håkan Juholt. In the Ipsos poll carried out on behalf of newspaper Dagens Nyheter, the Social Democrats have 29.7 percent of the vote.
Nonetheless, they appeared poised to form a new government as the nation's largest political party.
The ruling centre-right government Alliance parties together have 37.7 percent of voter support against the red-green opposition's 48.8 percent.
Rising in the poll over the 4 percent threshold to enter into Parliament is the Feminist Initiative, which rose 1 percentage point to just clear the barrier.
"It's too soon to count out (party leader Gudrun) Schyman" Ipsos' David Ahlin told the newspaper.
On Wednesday night, the party leaders met once again in a televised debate moderated by the newspaper Expressen. One topic that saw clashes between the Left and Liberal parties was whether profits should be allowed in Sweden's welfare system.
"The Difference between us and the Alliance is that we do not want schools and health care to be treated as a lottery," Left Party leader Jonas Sjöstedt said.
For the Ipsos poll, the right-leaning Christian Democrats and the Centre Party are again on the border between staying in parliament and dropping out altogether. While on the left, both the Green Party and the Left party have made gains.
The poll is based on 1,463 telephone interviews with elligable voters between August 22 to September 1.