Mr Dawes approved the purchase of the land last year, paying $4.2 million to developers Barry Morris and Graham Potts. Mr Dawes says the purchase did not need separate authorisation from the board because it related to the already approved City to the Lake project. He advised the board after the event, in September 2015.

Auditor-General Maxine Cooper said she planned to have the audit ready by the end of September, but the timing could be affected "by the need to share potential conclusions and findings with relevant parties".

In the ACT parliament on Wednesday, Mr Coe said the government had "seemingly paid $3 million more than what they had to and in addition to that they've not had a clear delegation or authority".

He said the only authority the Land Development Agency had to buy land was a July 2014 direction from Chief Minister Andrew Barr, which said purchases below $5 million needed agreement of the board and advice to the minister.

In August 2015, just before the finalisation of the Glebe Park purchase, the board had discussed how the 2014 direction from Mr Barr should be interpreted. The "preferred" interpretation endorsed by the board, according to board minutes, was that the direction applied only to land outside the agency's "core business" of delivering the land release program. The interpretation gave the agency the "necessary flexibility to pursue opportunities as they arise" without compromising transparency, the board minutes said.

Mr Coe said it appeared the agency "didn't like" the government's land acquisition policy and had "established a way to determine when this direction from the minister does not apply".

"How the LDA can delegate away the minister's direction is beyond me," he said. He also pointed to three other land purchases in December 2014, January 2015 and June 2015 that he said did not comply with the ministerial direction.

"At best this is sloppy governance, at worst it is a very serious matter," he said, accusing the agency of "overstepping the mark".

"The direction states that the LDA board must approve acquisitions under $5 million but that seems to have been ignored," he said. "We know that because the head of the LDA has advised us that he informed the board after the acquisition was made ... The board appears to have been sidestepped by the agency and the responsibilities of the board members seems to have been compromised."

The agency got two valuations for the land, one putting the value at about $1 million and the other at $3.6 million to $3.8 million plus GST. Mr Coe questioned why there was not a third valuation.

Mr Barr said Mr Dawes had assured the government that the purchase "was conducted in accordance with his delegation, which requires agency funds to be used efficiently, ethically and effectively".

He had judged two valuations were sufficient because the price negotiated fell "within the range" of the two.

No agency staff had declared a conflict of interest over the purchase, Mr Barr said.

The City to the Lake project was "a game changer for Canberra", like the Southbanks in Brisbane and Melbourne. Of 15,000 people surveyed in 2013, 94 per cent supported the lakefront redevelopment and the reconstruction of Parkes Way. That compared to just 200 opponents at a public meeting in July this year, he said.

The only way to fix the "bad, bad" mistake of a freeway between the city and the lake was to redesign Parkes Way. The stormwater pond at the roundabout had to be relocated to increase the size of the block opposite the CIT for sale, to reduce congestion at the intersection, and to improve water quality flowing into the lake, he said.

The Greens Shane Rattenbury voted with Labor to defeat Mr Coe's call, saying the case was being properly investigated by the auditor-general who would do an objective, thorough and complete review and clear up any questions.