Åkerlund,64, made the statements on his party's community radio show back in 2002. He gave his views on a monthly radio slot using the false name 'Viktor' where he spoke widely about immigration and refugees.
"We should return 500,000 of the most obvious and worst parasites…those who are in Sweden for no other reason than to exploit us financially," said Åkerlund 11 years ago.
He added that deporting foreigners would boost Sweden's economy and suggested that most of the bullying carried out in Swedish schools was done by immigrant children.
"It was 11 years ago. I was not so mature at the time," Åkerlund, who was 53 when he made the comments, told Aftonbladet.
He added; "I was not so mature politically…but I said many terrible things at that time that I don't stand behind today."
The leader of the Sweden Democrats, Jimmie Åkesson, said his deputy's choice of words back in 2002 was "unacceptable."
"It is of course very unacceptable language. Jonas has made it clear that this is not something that he stands for today and that it was a reprehensible choice of words that was said almost 12 years ago," said Åkesson to Aftonbladet.
Åkerlund has been involved with politics since the 1970s when he was active in the Social Democrats. He switched to the Moderate party (Moderaterna) in the 80s before moving to the Sweden Democrats in 1995.
He has been a member of the Swedish parliament since 2010 after being elected in the Blekinge constituency in southern Sweden.
The press spokesperson of the Sweden Democrats said that the party was keen to move on from the latest scandal and that the matter had been settled following a meeting between Åkerlund and leader Jimmie Åkesson.