The Greens are demanding Wilson Security be barred from rebidding for work at the Nauru immigration detention centre after claims one of its senators was subject to systematic spying.

An unnamed whistleblower alleges Sarah Hanson-Young had her every move tracked by a team of eight Wilson guards while visiting the island in 2013, a claim at odds with evidence the company has given to a Senate inquiry.

The former guard told ABC TV that management had ordered his colleagues to shred pages in their notepads and any reports they had written.

The Greens leader, Richard Di Natale, has urged the Australian federal police to investigate the claims, despite the visit occurring outside its jurisdiction.

“Can you imagine if a member of the government or opposition was spied on in the same way?” he asked reporters in Canberra on Friday. “Heads would roll.”

Di Natale called for the immigration minister, Peter Dutton, to apologise to Hanson-Young for initially ridiculing her complaint.

“Unless there is a full independent police investigation of this matter then the minister needs to consider his position,” Di Natale said.

Wilson Security apologised to the senator during a hearing of the inquiry, insisting the spying had been limited to the unauthorised actions of a rogue individual.

Di Natale accused the company of giving misleading evidence, possibly putting it in contempt of parliament.

“We can’t have this lawless government contractor responsible for the security of innocent people,” he said.

Hanson-Young is seeking legal advice.

