Greens senator Sarah Hanson-Young has attacked Prime Minister Tony Abbott for suggesting guards who allegedly spied on her in Nauru were taking care of her, saying that any woman would find it "creepy" to be monitored.

However, Immigration Minister Peter Dutton has accused the senator of "attention seeking" and said she was an "embarrassment to our country".

Senator Hanson-Young earlier asked how Mr Abbott would feel if his wife or daughters were being monitored while going about their work.

A former security guard has alleged in a submission to Parliament that Senator Hanson-Young was covertly followed when visiting the Nauru detention centre in 2013 and was codenamed "Raven".

The company that hired the private security guards, Wilson Security, has rejected the allegations but admitted some contractors had been disciplined for going "beyond their brief".

Mr Abbott on Friday said he did not "accept that characterisation" that Senator Hanson-Young had been spied on.

"I believe she being, in fact, looked after while she was there," he said.

Senator Hanson-Young said the allegations were "deeply concerning", adding: "The Prime Minister - the Minister for Women indeed - if he doesn't understand that women don't like to be watched, my gosh, and it is just creepy, frankly. It is creepy.

"Women don't like to be watched.

"The fact that the Prime Minister, the Minister for women, doesn't seem to understand that beggars belief.

"I'd like to ask the Prime Minister how he would feel if his wife was being watched. How he would feel if his daughters were being watched going about their work."

Senator Hanson-Young said she feared there may have been a "serious breach of the law" and has referred the matter to the parliamentary privileges committee.

It is "frankly illegal" to spy on a politician doing their job, she said.

Mr Dutton said he did not have any evidence Senator Hanson-Young had been spied on.

"I have evidence that Senator Hanson-Young over-states every issue. She gets her facts wrong most of the time. And I just think you need to look at it in the light of experience with Senator Hanson-Young," he said.

"If she's got evidence, produce it."

Senator Hanson-Young said she sensed she was being followed when she visited Nauru in 2013. She has since been contacted by other service providers who had been told she was being monitored.

Senator Hanson-Young said she had tried to make light of the matter by changing her Twitter name to "The Raven" on Friday.

"This is pretty amateur hour stuff - the idea that I was tagged as 'The Raven' over the radio waves," she said.