Problems inside a flagship counter-terrorism police unit "would concern all Australians", Federal Labor has said, after revelations the unit was prevented from engaging with extremists because it did not have a car.

The ABC has obtained documents showing the Australian Federal Police deradicalisation unit did not have its own vehicle in Sydney for months until mid-last year.

"I'm appalled if the Government has been incompetent," Opposition Leader Bill Shorten said.

"Countering violent extremism should have all the resources it needs to be thrown at it.

"You can't do that on the cheap."

The AFP Diversion Team aims to intercept homegrown extremists and turn them away from terrorism.

It refers radicals to state and territory countering violent extremism (CVE) coordinators who direct participants towards programs and services.

A report from June 2016 said being forced to share cars "[continued] to impact on [the team's] ability to engage with participants".

Another document said the team struggled to recruit psychologists to assess the risk posed by extremists and to recommend suitable programs.

The unit was established in November 2014 as part of a major Abbott government counter-terrorism package.

Despite the frustrations expressed privately, an AFP spokesman insisted the Sydney staff member had access to "pool vehicles".

The spokesman said the countering violent extremism squad now had a car primarily for its use.

Crossbench senator Nick Xenophon said the situation was "just crazy" and offered to lend the team a hand.

"I'm going to chip in right now for them to have a hire car for whenever they need it," Senator Xenophon said.

"I'm sure there are enough members of Parliament who'd chip in for a hire car, if that is the state of their budget.

"I thought that we had sorted out those budget issues … to keep Australians safe."