Prime Minister Tony Abbott is mocking suggestions the Government should have an open tender process for Australia's next fleet of submarines, saying that could result in "Kim Jong-il-class submarines" or "Vladimir Putin submarines".

The Government has been under pressure over how it will award the multi-billion-dollar contract since it emerged the Prime Minister had reassured a Liberal MP that Australia's shipbuilding company would be allowed to compete in the lead-up to this week's vote on his leadership.

Mr Abbott said the Government would use a "competitive evaluation process" to make the decision.

But the MP in question, South Australian Liberal senator Sean Edwards, earlier this week said the Prime Minister had described it to him as an open tender process.

In Question Time, Opposition Leader Bill Shorten asked: "If the Prime Minister did not promise Senator Edwards a full and open tender, what precisely did the Prime Minister promise to obtain his vote?"

Mr Abbott stood by his description of the process as one of "competitive evaluation" and accused the Opposition of wanting to allow "anyone to be able to compete".

"He might want the Russians to compete - the Putin subs is what we will get from the Leader of the Opposition," Mr Abbott told Parliament.

"We could have Kim Jong-il-class submarines, Vladimir Putin submarines.

"You cannot trust the Opposition with the defence of this country but you can with this Government."

Simple assurance given for Australian contractors: Edwards

Earlier this week, Defence Minister Kevin Andrews came under pressure to define the competitive evaluation process but offered no further detail other than to say it would consider technical aspects, cost and timing.

Senator Edwards also addressed Parliament on Wednesday and said he had been reassured that Australian contractors would be able to bid.

"Putin subs is what we will get from the Leader of the Opposition" - Tony Abbott ( Reuters: Aleksey Nikolskyi )

"For the avoidance of confusion and doubt that has infected some in this place, I don't mind what you call the process," he said.

"Such specific terminology was never part of the assurance I sought. The assurance I sought was very simple. I asked for Australian companies like ASC to have the right to compete for the Future Submarine project on merit.

"That's the very assurance I got."

Senator Edwards has not backed away from his recollection of the conversation with the Prime Minister but said all that mattered to him was that local shipbuilders could compete.

The new submarines were expected to cost up to $40 billion.

ASC employs about 2,000 people and its future is said to rely heavily on involvement in the submarine contract.

Late last year then-defence minister David Johnston came under fire for declaring that ASC could not be trusted "to build a canoe". He was dumped to the backbench shortly after.