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Colin Barnett has set the scene for an uncomfortable relationship with the Commonwealth Government if Julia Gillard wins the Federal election, after questioning her authority and authenticity as Prime Minister.

The Premier said the manner in which Ms Gillard obtained the top job offended Australians' sense of fair play.

"The way in which Julia Gillard replaced Kevin Rudd is something that has not been well accepted by the Australian population," he said.

"Australians have a very fine sense of fair play and they do not see fair play in that. That is why her campaign is being dogged and it's not going to go away.

"It's my view that a lot of people are going to decide their vote on that, because she lacks legitimacy as a Prime Minister and Julia Gillard lacks authority as a Prime Minister."

Mr Barnett is in dispute with the Federal Government over issues including health, the GST and the housing of asylum seekers in WA.

Although he frequently clashed with Mr Rudd over policy, he sympathised with him after he was axed.

Mr Barnett has previously said he believed the former prime minister had a better understanding of WA while Ms Gillard is Eastern States-centric.

Yesterday, Mr Barnett revealed he would take part in about 15 events in support of Liberal Party candidates in coming weeks.

"It seems to me that Tony Abbott has done very well over the last week or so, so it’s going to be close," he said.

"I expect the Liberal Party may now gain some ground. Whether they will gain enough ground to defeat a first-term Government, who knows."