Labour MSP David Stewart, whose Highlands and Islands constituency includes Moray, has joined Liberal Democrat Tavish Scott in questioning the franchise.
Their move follows the recent departures of leading Abellio executives amid investigations into the awarding of a public transport contract in Holland which had also been won by the firm.
Mr Stewart and Mr Scott are the respective spokesmen for their respective parties at Holyrood. Both insist that SNP ministers at the Parliament have “very serious questions” to answer about the award of the rail franchise.
Mr Scott said: “The Scottish Government should initiate a full independent inquiry into the award of the rail franchise to Abellio.”
Meanwhile David Stewart confirmed he had called for a discussion on the issue: “I have lodged a motion seeking cross-party support to have a debate on this matter.”
However, a spokesman for the Scottish Government last night insisted there was “no suggestion” of misconduct.
He said: “There is no suggestion of any conduct that puts the ScotRail franchise procurement process in doubt – reviews of Audit Scotland and independent auditors have supported the outcome.”
Two senior Abellio executives were last week dismissed from their posts after accusations of inaccurate and incomplete statements over the awarding of franchise in Holland.