The £745 million project is due to be completed in the spring following a previous delay, but MSPs are concerned the date could be pushed back to later in the year.
Carillion formed one third of the Aberdeen Roads Ltd (ARL) consortium leading the work alongside Balfour Beatty and Galliford Try.
While Keith Brown said the remaining two firms were committed to completing the project within the current timescale, discussions were needed on the potential impact of supply chain issues as a result of the construction giant’s demise.
Mr Brown was questioned on the AWPR’s progress during a meeting of Holyrood’s Rural Economy and Connectivity Committee.
Conservative MSP Peter Chapman asked if the road would be completed by the end of May, while Liberal Democrat MSP Mike Rumbles suggested it could be “drifting towards the summer”.
Mr Chapman said: “I have concerns I must admit... I see the amount of work that is ongoing and I also see the amount of work that’s still to be done, and I just have severe doubts as to whether we can ever meet even that May target.”
Mr Rumbles said: “Drivers, commuters and people who live in and around Aberdeen and need to use this route need to know for their own planning purposes when ministers think this project should be completed.
“If it’s drifting towards the summer I think we should say so, let people know that.”
Mr Brown said: “Whilst the situation with Carillion does not in itself affect project delivery timescales, members will appreciate given the scale of this issue, and the potential for a loss of confidence in the supply chain... it is important that we now take the necessary time to work closely with ARL to identify any impacts that they can identify on delivery.
“We will then consider what we can do to mitigate any issues that may arise as a consequence of that.
“That might take some weeks to determine.”
He said the spring opening was still anticipated, adding “we have no intention of trying to change that date”.
However he said: “We are coming towards the end of this, we can’t be definitive until we have that discussion with the developers about the latest situation with Carillion, but as soon as we do have that date I am happy to provide it to the committee.”