Fingerprint clue in threat against Lambie

Independent Senator Jacqui Lambie is expected to address the upper house about the recent threat to her life, as police investigate a suspect fingerprint lifted from the correspondence.

A letter addressed to the Tasmanian senator's Burnie office last week threatened to behead the 44-year-old politician unless she converted to Islam.

Tasmanian police have told Senator Lambie of a breakthrough in their investigation, her chief of staff Rob Messenger told AAP.

"It was explained as half a fingerprint from the handwritten envelope and they are now doing checks to rule out that it belongs to a staff member who handled the envelope when it arrived at the office," he said.

The letter was posted in Adelaide where investigations are also underway.

Senator Lambie will make a speech to parliament in reaction to the death threat, either on Tuesday afternoon or Thursday, Mr Messenger said.

"In the meantime it's business as usual for the senator."

Security measures will be boosted at the senator's Tasmanian office in light of the threat, Mr Messenger said.