"We must force the other parties to cooperate with us," Åkesson said in a speech during the Swedish parliament's conference on the future on Saturday.
The early years were marked by xenophobia and the party had connections to the white power movement.
Åkesson has said that he is not proud of this part of the Sweden Democrats' past.
"The party leadership spoke about this radicalization as something positive and it was allowed to characterize the party for a long time, with skinhead demonstrations and the like," said Åkesson.
"There was a period of three or four years when we had these serious problems. Of course it should never have happened, but at the same time we are where we are now, despite everything."
Despite a turbulent, scandal-ridden period last autumn when several top Sweden Democrats were forced to resign, Åkesson believes the party is now strong.
"We are doing fantastically well, I think, considering our membership numbers have grown significantly and we are doing very well in opinion polls. We have never done this well," Åkesson told the TT news agency.
Asked what problems he believes the party has, Åkesson replied that he prefers to speak of "challenges".
"For example, we know that there is a powerful polarization in Swedish politics now where many absolutely cannot imagine voting for us. I think that group has shrunk quite a lot in the past six months. Today, 20 percent of Swedes say they could imagine voting for us, but there are still too many who dislike our party," said Åkesson.
He put that down to the fact that there is a "distorted picture" of the party and that many dislike it on the wrong grounds.
"We have to be very clear about where we stand and be clear in our opposition to extremism. We have to take a clear stance against crazies representing the party and we also have to raise issues so that these voters understand that this is a party for them too."
Since the 2010 general elections, the Sweden Democrats have expelled 30 members. In the same period, the other parties in parliament expelled five members altogether, according to research by Sveriges Radio (SR).
Sweden Democrat party secretary Björn Söder said the high number of expelled members can be explained by the fact that the party has grown rapidly in a short period.
"Representatives or members who we may not have known enough about have been able to get elected. We have then noticed that they were not appropriate representatives of the party," said Söder.
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