The Police Union's criticism comes after reports that one of the party leader's wedding guests has ties to the criminal motorcycle gang environment.
In an interview with TT, Chairman Katharina von Sydow calls the reports both remarkable and worrying.
Gunnar Strömmer (M) says he understands the criticism.
There is always reason to listen to the police. This applies to this issue and all issues. It's easy to understand why the questions are being asked, he says.
"Must answer himself"
The Minister of Justice, on the other hand, does not want to explicitly criticize Åkesson, whose Sweden Democrats are part of the Tidö cooperation together with The Moderate Party, The Christian Democrats, and The Liberals.
Jimmie Åkesson must answer the criticism himself. He has acknowledged that this was a failure, and there's a lot to that, he says.
"A failure"
Jimmie Åkesson has commented on his actions, saying he was not aware that the man held a leadership position in Comanches, a motorcycle gang that the police consider a criminal network.
Earlier on Wednesday, Prime Minister Ulf Kristersson stated that it was inappropriate behavior.
I have no other opinion than the one Jimmie Åkesson has expressed, that this was inappropriate, of course, he told Sveriges Radio.