Take responsibility for Oceanic 78: Barnett

Australia needs to take responsibility for the 78 asylum seekers on a customs ship in Indonesian waters, says Premier Colin Barnett.

Despite his Federal coalition colleagues believing the asylum seekers should not enter Australia, Mr Barnett told ABC Radio the matter needed to be dealt with promptly.

Ethnic Tamils have spent weeks onboard the Australian customs vessel Oceanic Viking after they were rescued in Indonesian waters.

The asylum seekers have threatened suicide and refused to leave the boat, which has been anchored off the Indonesian island of Bintan for more than two weeks.

Mr Barnett acknowledged there was no easy solution, but Australia "needs to deal with it".

"I don't think Australia is doing itself any good at all by having 78 asylum seekers on an Australian quasi naval boat in Indonesian waters," Mr Barnett said.

"We are almost letting our immigration policy be dictated to by the Indonesian government.

"Well, come on Australia, we've got to take responsibility.

"I don't like this solution, but I think Australia has really little option but to take them to Christmas Island ... sort them out, find out who might be genuine asylum seekers, who are not, and deal with it."