In a marked escalation of the stand-off between unions and the newly nationalised rail operator, Mick Hogg, the Scottish regional organiser of the RMT, said Jenny Gilruth “holds the key” to a settlement.
Earlier on Monday, Ms Gilruth said she could not "put a number on" a reasonable pay offer in ScotRail’s impasse with Aslef, the train drivers’ union, as the decision must be left up to the firm and the union to negotiate.
Since April, the operator has been run by an arm’s length company that is owned and controlled by the Government.
But Mr Hogg called on Ms Gilruth to play a more active role in negotiations with Aslef and the RMT, and said it was disingenuous of her to suggest she could not do so.
"The buck stops with her,” he told The Scotsman. “She, as transport minister, holds the key to a settlement.
"She is telling lies when she advises she wants the unions and ScotRail to get round the table, as ScotRail senior management do not have the authority unless she gives it.”
With ScotRail hit by a raft of cancellations on the first day of its controversial reduced timetable, Aslef has also written directly to First Minister Nicola Sturgeon, calling for her to make a “positive political intervention” and show “leadership” over the dispute.
Its Scottish organiser, Kevin Lindsay, also condemned comments made by Ms Sturgeon’s ministers as “inflammatory, unreasonable, and factually incorrect”.
He described the pay negotiations to date as “shambolic”, and condemned Ms Gilruth for attempting to “lay the blame” at the door of the unions.
In his letter to Ms Sturgeon, Mr Lindsay went on: “We urgently need to see progress and a de-escalation of this situation. The Scottish public demand it. They need to get to and from work, leisure and important cultural and sporting events satisfactorily and this needs a full service that is invested in, not cut.
“We have said repeatedly we want to return to talks. We stand ready whenever they are called to meet with ScotRail and the Scottish Government anytime, anyplace and anywhere.
“Sadly, up until now there has been negative political interference. It is now time for positive political intervention and leadership from you with an instruction to ScotRail to enter as a matter of urgency meaningful pay talks with the full intention to sensibly settle these pay negotiations."
On Friday, Ms Gilruth said the new temporary timetable, which has culled around a third of weekday services, would “give passengers more certainty for the short term, rather than being faced with unplanned cancellations”.
David Simpson, ScotRail’s service delivery director, also said the new timetable would give its customers “a level of certainty and reliability.”
But as of 3:30pm on Monday, there were 21 cancellations on the first day of the timetable’s operation. Several were attributed to a shortage of train drivers, with other services were cancelled because of a “shortage of train crew”, according to ScotRail’s journey checker service.
Alex Cole-Hamilton, leader of the Scottish Liberal Democrats, described the situation as “an omnishambles dressed up as a bin fire”.
Even on many services which ran as scheduled, the number of coaches was reduced due to widespread staffing issues. The reduced coaches were blamed on a shortage of train crew, as well as a lack of drivers.
The scaled-back timetable will see almost 700 fewer trains running Monday to Friday due to the dispute with Aslef, which has rejected a 2.2 per cent pay rise.
It means the last train on the many routes will depart in the early evening rather than late at night. The last train from Glasgow to Aberdeen, for example, will now depart at 6:41pm, instead of 9:40pm. The Glasgow to Mallaig service, which usually leaves at 6:21pm, now departs at 12:22pm.
Aslef and the RMT, which has also rejected a 2.2 per cent pay deal, are both balloting their members for strike action.
Earlier on Monday, Mr Simpson said that compromise would be required on both sides of the negotiating table.
"The demands of 10 per cent to 11 per cent are just not sustainable in the current economic climate with the railway,” he told BBC Radio Scotland.
"We need to find a way around that. We need to recognise the kind of demands the unions are making, but also the need to demonstrate taxpayer value."
It comes as Downing Street has told rail unions to hold discussions with the UK Government before causing "irreparable damage" with possible strike action.
A national ballot of more than 40,000 RMT members across Network Rail and 15 train operating companies is in its final days, with the result of the vote expected on Wednesday. The RMT said the action was being taken over pay, compulsory redundancies and safety concerns.
Prime Minister Boris Johnson's official spokesman said: "Railways are going through difficult times with passenger numbers down. We need to make sure they're fit for the future.
"We want a fair deal for staff, for passengers and taxpayers so money isn't taken away from other essential services, NHS being a good example.
"The prime minister is firmly of the view that unions should talk to the government before causing irreparable damage to our railways - strikes should be the last resort not the first."
ScotRail and Transport Scotland have been approached for comment.