Indigenous leader Pat Dodson has been elected as a new senator for Western Australia, saying it is important for the public to witness such events.

Mr Dodson will fill a casual vacancy caused by the departure of Labor's Joe Bullock, who resigned over his party's support for same-sex marriage.

He was been nominated to the position by Premier Colin Barnett and seconded by Opposition Leader Mark McGowan, who met him on arrival this morning.

After the joint sitting, Senator-elect Dodson said he wanted to work to ensure all West Australians enjoyed the same quality of life.

"I want to ensure that people in the remote areas and in the northern areas of Australia are also able to enjoy the services and the quality of those services that we can enjoy in cities and other places," he said.

The Yawuru leader, known as "the father of reconciliation" said he hoped to collaborate with all members of Parliament on matters that effected WA and Indigenous people.

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"In particular the constitutional recognition of the first peoples of this nation, and getting to a stage where our nation can put behind us those causes of division and discord that have so divided so many of us from enjoying the fullness and the fruits and the benefits that this nation's got to offer."

Premier Colin Barnett told MPs Mr Dodson was worthy in every way to fill the position and would be a powerful voice for Aboriginal people.

Mr Dodson sat in the president's gallery on the chamber floor during the joint sitting.

Labor's Indigenous affairs spokesman Ben Wyatt said Mr Dodson would serve the Senate with great distinction.

Labor Kimberley MP Josie Farrer said he was a powerful advocate for justice and human rights.

Deputy Opposition leader Roger Cook praised Mr Dodson for his "patience, respect, resilience" when they worked together for Indigenous reconciliation.

"Today, the Senate's stature is raised by the election of Patrick Dodson," Mr Cook said.

Pilbara MP and former Nationals leader Brendon Grylls also strongly praised Mr Dodson.

"Thank you Pat Dodson for what you have done until today," Mr Grylls said. "And Pat Dodson, go well in the Australian Senate."

Same-sex marriage controversy erupts

However there was a brief controversy as Southern Rivers MP Peter Abetz took the opportunity of an open floor to proffer an anti-same-sex marriage speech, and attack Labor's position.

"I'm sure that Patrick Dodson has been used to being a very free voice in the community. Speaking his mind and espousing traditional Aboriginal social values," he said.

"And no doubt he will find it challenging at times to toe the party line."

But when Mr Abetz began to comment on traditional marriage customs in the Indigenous community, he received groans from the chamber and calls of "shame" from the public gallery, while Nationals MP Brendon Grylls walked out of the chamber in apparent disgust.

Mr Abetz was eventually called to order by the Speaker, who questioned the relevance of his comments, sparking applause within the chamber, and from the public gallery.

Senator-elect Dodson did not believe Mr Abetz's comments had overshadowed the joint sitting.

"I don't think it detracted from it at all," he said.

"You'd say it was bad taste, but we live in a democracy. It's a parliament and people have got a right to say what they want to say."

He expressed his support for same-sex marriage, saying no one should be discriminated against.

Mr Barnett apologised to Mr Dodson for his backbencher's comments, and said while everyone was entitled to their view, today was Mr Dodson's day.

"I was disappointed in the comments Peter Abetz made," the Premier said.

"I think it was inappropriate for that reason. I did speak to Pat after and apologised if it caused him any embarrassment. He assured me he didn't and it didn't spoil his day.

"It wasn't appropriate. It wasn't the time or place to debate gay marriage."

Special sitting of Parliament 'unusual'

Mr Barnett acknowledged the Parliament ratifying Mr Dodson as a new senator in a special joint sitting of Parliament was unusual.

"It's a fair a proper thing to do, and the State Government is, and the Parliament is, cooperating with the Labor Party in Canberra to make this appointment be in place quickly," he said.

The sitting comes in the middle of a four-week parliamentary break, and has been scheduled to ensure Mr Dodson can take up his spot in the Senate before Federal Parliament resumes.

That would mean Mr Dodson would sit in the Senate for just a few days, if Prime Minister Malcolm Turnbull opts to call a double dissolution election for July 2.

The sitting of WA Parliament to appoint Mr Dodson is expected to come at a substantial cost because of travel requirements for regional MPs. Some MPs are unhappy and labelled the sitting "a waste of money".