Senator threatened after number leaked

Jacqui Lambie says she has received abusive and threatening phone calls since her number was leaked. (AAP)

Independent senator Jacqui Lambie says she has received a number of threats today after One Nation senator Malcolm Roberts leaked her private phone number on social media.

Senator Lambie said she will have to change her number to keep her family and friends safe given the ease with which people can find personal information from a phone number.

"I have received many nasty, abusive and threatening phone calls and messages," she told parliament.

"You have the (federal police) briefing politicians about our safety, you have gallows on the steps of Victoria's parliament and senators in this very chamber should not be facilitating any abuse."

Changing her number would affect veterans with poor mental health and who are on their last legs, Senator Lambie said.

"Those veterans know they can call me at any time of the day or night if they need someone to listen to them.

"It is completely unacceptable to leak other senators' personal contact details to the public just because you do not like what they are saying.

"One Nation have crossed a line here that should never be crossed."

Senator Roberts told the Senate that One Nation's Tasmanian Senate candidate Steve Mav posted the number after being sent it by a voter who got it from a Facebook post from Senator Lambie urging people to contact her.

Appearing via videolink, Senator Roberts accused Senator Lambie of playing the victim and misrepresenting the circumstances - which was met by her shaking her head in the chamber.

Senator Lambie asked Senate President Slade Brockman to investigate the leaking of her number and decide whether Senator Roberts should issue an apology, as well as looking at the safety of senators more broadly.

Senator Brockman is considering both matters.

The revelation came on the same day two men who allegedly left threatening messages on the phone of West Australian Premier Mark McGowan are facing charges.

The premier's personal phone number was leaked last month and he was forced to close his electorate office south of Perth indefinitely amid security concerns.

"There's been death threats, there's been threats to rape my staff, there's been people threatening to bomb my office," he said.

It also comes a day after Australian Federal Police Commissioner Reece Kershaw said the force was on high alert following threats against high profile politicians in recent weeks.