The Morrison government's bill to establish a national commissioner for defence and veteran suicide prevention is short of the support it needs to pass the Senate.

A Liberal-chaired Senate committee has called for the legislation to be supported but recommended the government consider whether the commissioner should cover attempted suicide.

The report also encourages the government to consider reviewing the role and look at the importance of independence in recruiting the commissioner.

Labor and Senator Lambie both issued dissenting reports calling for the bill to be opposed in the upper house.

"This is a bill that's supposed to help veterans and their families. But families don't want this. Veterans don't want this," Senator Lambie wrote.

The former soldier believes a national commissioner is a poor substitute for a royal commission.

"The most egregious flaws with this proposal are structural and irredeemable," the Tasmanian independent said.

Senator Lambie said the commissioner would be subject to government power and influence, while a major inquiry wouldn't be worried about ongoing survival.

Labor senators Tim Ayres and Kimberley Kitching are concerned the commissioner could become a glorified coroner holding hearings in secret.

The opposition report echoes Senator Lambie's fear that families of veterans have been ignored in their calls for a royal commission instead of the new role.

"This is an important litmus test and a damning indictment on the bills, and it highlights precisely why they should not be passed," the Labor senators wrote.

One Nation's two senators back the new commissioner but the government remains one vote short of securing support for the legislation.

Australian Associated Press