The 2004 incident led to a souring of the relationship between Canberra and Timor-Leste, as the two nations were negotiating a deal on accessing offshore oil deposits at the time, the Australian Broadcasting Corporation reports.
Last month, Mr Wilkie used parliamentary privilege to reveal the Commonwealth Director of Public Prosecutions had lodged criminal charges against Canberra lawyer Bernard Collaery and a former spy known as 'Witness K' for divulging information about the operation.
But yesterday the Tasmanian MP said senior government officials were the "real criminals — the people who ordered the illegal bugging".
"There's no way the Police Commissioner can ignore a referral from three Australian senators and one Member of the House of Representatives," Wilkie said.
"Today is a day of reckoning."
Wilkie has enlisted the support of Tasmanian Greens senator Nick McKim and South Australian crossbenchers Tim Storer and Rex Patrick in referring the matter to the AFP.
"We wish the police to conduct an investigation to look at who's involved, who the senior officials are, who the government ministers were, noting all of this has been done in secret," Wilkie said.
"No-one is above the law."
Collaery, who is a former ACT attorney-general, has described the charges against him as "heartbreaking".
A conviction would mean he would be prevented from practising law.
He has fiercely criticised Attorney-General Christian Porter for allowing the charges to be laid, describing the whole process as a threat to freedom of speech.