The parliamentary group of the anti-Islam, anti-migration Alternative for Germany, the Bundestag's largest opposition party, told AFP it sacked Christian Lüth “with immediate effect” after it emerged he made the incendiary remarks.
News website Zeit Online had reported earlier that Lüth was speaking with a right-leaning YouTube reporter in February and was secretly filmed by a commercial broadcaster.
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In the conversation, he welcomed the fact that “even more migrants” were coming to Germany after it took in more than one million asylum seekers during the 2015-16 refugee influx because it would benefit the AfD politically.
“We can still shoot them all to death afterwards. That's not a problem,” Lüth is quoted as saying.
Or gas them, or however you want. I don't care!”
Zeit Online said the broadcaster with the tape, ProSieben, only identified the speaker as a high-ranking AfD official without naming him.
But the website said several informants told it the speaker was Lüth. The video is to be broadcast on German television later Monday.
ProSieben said the man was trying to convince the journalist he was speaking to to work with the party.
“The worse Germany is doing, the better for the AfD,” he is quoted as saying.
Two months after the meeting, Lüth was reportedly suspended after he described himself as a fascist and praised his “Aryan grandfather”.
Lüth's grandfather was a submarine commander during World War II and received an Iron Cross from Nazi leader Adolf Hitler, Zeit reported at the time.
As the migration issue has lost urgency in Germany, the AfD's support has slipped. It is currently polling at about 11 percent ahead of next year's general election to name Chancellor Angela Merkel's successor.