Premier Peter Beattie says he is not surprised there is criticism from within his own party about the Government's handling of issues on Palm Island in Queensland's north.

The local ALP branch has written a letter warning of waning support for Labor.

It is considering a protest later this month when Mr Beattie travels to the north Queensland Indigenous community to open a new gymnasium.

Mr Beattie says he understands there are strong views.

"If they want to have a protest that's fine with me," he said.

"I'm only interested in the long-term well being of the people of Palm Island.

"I think when these sort of circumstances happen of course there is going to be criticism of the government of the day and the premier of the day."

The Crime and Misconduct Commission (CMC) says it is continuing three strands of inquiries into events on Palm Island last year.

The CMC is assisting the inquest into the death in custody of a local man, while officers have also examined complaints about the police response to the riot which followed.

Investigations are also under way into accusations that the Indigenous Policy Minister's office asked Aboriginal leaders Murrandoo Yanner and Brad Foster to lie about airfares to the island.

The commission has previously said it would subpoena the two men if necessary.