A Tasmanian Senator says the Defence Force and the Department of Veterans Affairs are involved in a “cover-up of appallingly high levels of abuse”.

Palmer United Party senator Jacqui Lambie used her maiden speech to the Senate in Canberra to call for a national inquiry into abuse and sexual assaults in the military, the high solider suicide rate and a shortage of staffing and resources.

She recounted the story of Marcus Saltmarsh, an Iraq and Afghanistan war veteran who was accused and then exonerated by a military court of the accidental shooting death of a fellow soldier in East Timor.

Senator Lambie said Mr Saltmarsh was subject to a “complete failure of leadership” by departments, which meant he was never publicly cleared over the incident.

She said he was a “scapegoat” for the military to draw attention away from faulty rifles. She said the authorities leaked “adverse recommendations” to damage Mr Saltmarsh's “personal reputation and psychological wellbeing”.

“Mr Saltmarsh says this abuse could have been avoided if he had been able to be publicly exonerated,” she said.

“Because this government and Prime Minister – despite repeated written requests from myself - refuses to apologise for the appalling abuse Marcus has suffered, I'd like to apologise as a senator from Tasmania – his home state – for the incredible abuse and/or incompetence he's been forced to endure by certain leaders of our military.”

Senator Lambie also appealed for moves to fix the “outrageous, stinky, filthy injustice” of high transport costs between Tasmania and the mainland.

“If we are to be treated fairly as a state, the cost of people taking their cars, motor homes, camper vans, caravans, motorbikes, grey hounds, race horses or unicorns from Devonport to Melbourne or vice versa should be no more than the cost of driving the 327 kilometres of national highway from Melbourne to Albury,” she said.

“If the powers that control the Treasury benches in this place don't want an army of Jacqui Lambies in this place speaking uncomfortable truths and challenging them in the future, then fix the Bass Strait transport cost crisis.”

“The distance and cost of surface travel between Tasmania and the Australian mainland is a national disgrace, not a national highway. It's time to fix it.”