Initial estimates released in 2018 put the cost of the City to Woden leg of the project at between $1.3 to $1.6 billion.

However figures in the latest economic update reveal the bill for the project could balloon out to almost $2 billion.

It would put the cost per km for the 11km stretch rail at almost $173 million.

"The total cost for completing light rail stage two, including design, construction, purchase of additional light rail vehicles, an additional depot, and project management is estimated to be in the range of $1.5 billion to $1.9 billion," the update read.

"This will be influenced by prevailing infrastructure market conditions at the time of project procurement, National Capital Authority and Australian Parliament determined planning and heritage requirements through the parliamentary triangle and final detailed design of the project."

The update said $312 million was being set aside over the next three years for the project.

The complexities of the route have contributed to a much higher price tag than the $675 million spent on the 12 kilometre city-to-Gungahlin leg of the line.

Chief Minister Andrew Barr had previously called for the wire free sections of the light rail line to be limited to essential areas like the Parliamentary Triangle, to limit a price blow out.

However the latest submissions to the federal government show the route would also be wire free in the 1.7km stretch from Alinga Street to Commonwealth Avenue.

The government has refused to release full costings or cost benefit analysis for the project, citing commercial in confidence.

Transport Minister Chris Steel said an unredacted business case would not be released before the contracts were signed.

"This is to ensure the Canberra community receives value for money in the final contract," he said.

"We've released the business case and we've clearly outlined the cost of the total cost of the project - yet the Canberra Liberals still refuse to commit to support building light rail to Woden."

The figures are the first public update of the cost estimate of light right stage two since 2018.

Mr Steel attributed much of the price rise to a change of the route - which came about through federal government and National Capital Authority negotiations - bypassing Parkes and Barton.

He said the decision to raise London Circuit had also contributed to the increase.

The debate over light rail stage one dominated the 2016 territory election campaign, with the Liberals pledging to tear up contracts if they won government.

This time around, the Canberra Liberals say they would would conduct an independent analysis of the business case before signing contracts for stage two.

"Labor and the Greens want to spend almost $2 billion of taxpayers' money without being honest with the community about the details of this project," opposition transport spokeswoman Candice Burch said.

"This is almost three times the cost of light rail stage 1.

"ACT taxpayers deserve to know why the cost has blown out so much, and whether it will deliver value for money. Labor needs to come clean about the details of this significant infrastructure project."

The government says light rail stage 2A is estimated to return just 60 cents for every dollar spent on the project.

However it says once all of stage two is completed to Woden, the return for the whole stage will increase to $1.20 return on every dollar spent.

The government went to the last election promising to have the contracts signed for the second stage of light rail before the 2020 election.

However the contracts are yet to be signed, with Mr Steel blaming the delays on the coronavirus crisis.