David Lång sang along to techno hit L'amour Toujours, which has been co-opted by far-right groups in Germany in recent years, who have replaced the original lyrics with the Nazi slogan "Ausländer raus, Deutschland den Deutchen" ("foreigners out, Germany for Germans").
He sang "Ausländer raus" before spotting a reporter from the Expressen newspaper, who was interviewing another member of the party.
"Oh shit, are you recording this?" he said and then tried to grab the recording equipment from the reporter, before being asked to leave.
His actions were widely criticised, including within the party, and Sweden Democrat group leader Linda Lindberg said on Monday that he had chosen to resign from his parliamentary position on her urging.
"He has been in parliament since we entered it in 2010 and has done a lot of good for the party. That does not detract from his reckless actions [on Sunday], which he understands," she said in a statement.
Lång himself said he regretted the incident.
"I picked up this song on social media. I now understand that the lyrics have been sung in contexts that I so far have had no deeper knowledge of. It wasn't premeditated on my part and I am sorry if anyone was offended," he said in a statement.
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