The operator has reduced weekday and Saturday services by one third since last week in an attempt to give certainty to passengers after most drivers stopped working overtime, but it said it had been unable to introduce a reduced timetable on Sundays.
Some 320 services were cancelled on Sunday as a result – 29 per cent of the 1,088 due to have run – with no advance warning.
Ms Gilruth said that was “far from ideal”.
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She said: “Because drivers continue not to work their rest days, as is their right and their choice, services were disrupted on Sunday.
“I know that has inconvenienced and frustrated many travellers.
"ScotRail will continue to look at what more can be done to improve weekend service availability.”
However, Ms Gilruth said the indefinite temporary timetable was providing a reliable service and carrying some 90 per cent of the passengers who travelled before it was introduced on 23 May.
ScotRail added extra late evening services on routes across the Central Belt last Friday and Saturday, which will continue this week.
They will also run on Wednesday to help take fans home from the Scotland v Ukraine men’s World Cup football tie at Hampden in Glasgow.
These include last trains on the Glasgow-Edinburgh main line at 11.45pm, as they were before the timetable cuts.
The last services from Glasgow to Stirling, Ayr, Gourock, East Kilbride and Neilston will leave after 11pm.
However, ScotRail has pointed out that the last trains to stations further afield, such as Dundee and Aberdeen, would have departed before the final whistle even under the normal timetable.
The drivers are considering a revised 4.2 per cent offer made by ScotRail last week after their union Aslef rejected an initial 2.2 per cent deal and called a strike ballot.
Scottish Conservatives transport spokesperson Graham Simpson said that even if they accepted the offer, it would take three weeks for a ballot to be held, during which the disruption could continue.
However, Ms Gilruth said the issue could be resolved on Wednesday when the offer is put to Aslef’s executive committee.
Mr Simpson said: “It was carnage on the railways at the weekend.
"On Sunday, 320 services were cancelled.
"There may be more this Sunday.”
Meantime, the RMT, which represents ScotRail staff such as train conductors and ticket examiners, is to consider a similar 4.2 per cent improved pay deal to that offered to drivers following further talks with the company on Wednesday.
The union had also rejected the original 2.2 per cent offer and was planning a strike ballot.
The RMT is still to announce whether it will order strikes at 15 other train operators, including cross-Border firms, and Network Rail over a separate pay dispute.ScotRail said any walkout by Network Rail signallers would have a “massive impact” on its services.
Network Rail said some trains could run in and around Edinburgh and Glasgow as managers could operate the cities’ signalling centres.