A document submitted to the Scottish Parliament by contractors Balfour Beatty and Galliford Try said completion of the crossing would allow for the “opening of the full project” but that the contractors’ losses will be “huge”.

The paper was lodged with Holyrood’s rural economy and connectivity committee ahead of a meeting today where contractors were grilled by MSPs amid mounting concern over the delays and costs to the Aberdeen Western Peripheral Route (AWPR).

It was also revealed that a major section of the bypass will open next week after a contractual dispute was finally resolved.

The 20-mile southern section between the A90 at both Stonehaven and Craibstone and the A956 between Cleanhill and Charleston was completed in October but its opening was delayed due to a disagreement between the Scottish Government and joint venture Aberdeen Roads Limited (ARL).

It is understood negotiations have now been concluded, and the contractors are expected to open the significant section within days. This development means more than 85% of the project will be open to traffic.

The contractors also said the River Don Crossing and the other unopened sections of road will open by Christmas, unless there is adverse weather, though snagging work is to continue until March.

The document states: “The remedial works (on the Don Crossing) are currently forecast to be complete just before Christmas, which would allow opening of the full project – albeit that is a challenging programme as the works are highly susceptible to adverse weather, and are subject to stringent safety tests.”

“Even after resolution of the claim, the joint venture partners’ losses will be huge,” the document added.

During today’s meeting, Balfour Beatty major projects managing director, Stephen Tarr, Galliford Try’s construction and investment chief executive, Bill Hocking and ARL director, Brian Love were asked by North East MSP Mike Rumbles if the £745m project had now run into the hundreds of millions.

Mr Tarr replied: “Yes, you could deduce this.”

He added the three firms hope to recoup some of that from Transport Scotland, but refused to say how much was being claimed.

Mr Tarr said: “Within the last 24 hours we can confirm we have secured lender consent to the contract variation which paves the way for this section to be open next week and we’re working to complete the works at the Don Crossing later this month.”

He added: “One of the most significant (issues) is the early work with the utility providers.

“The claim we have stems from delays and underperformance due to that work. It’s those delays that have disrupted the progress of the work. Those issues lie at the heart against our claims.”

Mr Hocking said: “These delays (in opening the Craibstone-to-Stonehaven section) have cost us £4m. We have a very strong interest in opening the road as soon as possible.”

Mr Tarr added: “We are hundreds of millions out of pocket for the work we have done in Aberdeen. It’s a serious financial situation that we’re in. I can tell you it’s not a very comfortable feeling on this side of the table.”

Transport secretary Michael Matheson expressed delight that the section of the project will open next week following weeks of “intensive talks” but asked why his personal intervention was required.

Mr Matheson said: “This is the news we have all been waiting for. I have explored every possible avenue with Aberdeen Roads Limited to open this section of road as soon as possible and I am delighted my efforts to bring this matter to a positive conclusion have been successful.

“I made it clear to them my strong desire to get the road open would not be at any cost and Scottish Ministers are simply not willing to pay over the odds for the road on account of mistakes or miscalculations that are of the contractors’ own making. I am pleased they have now recognised this.

“It is disappointing my personal intervention was required in order to move this matter forward. I question why it has taken ARL this long to release these benefits to the North East when the road has been ready to open on October 5 and payments to ARL could have commenced earlier.

“I am sure the people of the North East will join me in a sense of relief and even excitement that a large part of this transformative road is finally opening. But they will also share my deep sense of frustration at ARL’s misguided and ultimately pointless tactics.

“We should also keep in mind that technical issues with the Don Crossing are the sole reason the road is not open today.

“ARL has said it aims to finish the bridge before Christmas but has also correctly warned the remaining works are complex, very weather sensitive and subject to safety and quality tests. We should therefore treat this optimistic programme with caution.”