The union’s national executive committee said on Wednesday it had thrown out the new offer, six days after it was tabled by ScotRail.
That followed an initial 2.2 per cent offer being rejected by Aslef, which led most drivers to stop volunteering to work overtime, on which services depend, especially on Sundays.
ScotRail has indefinitely cut 700 trains a day as a result since May 23, or about one third of the timetable, as The Scotsman was first to report.
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Aslef Scottish organiser Kevin Lindsay said: “Aslef wants to negotiate a fair deal for our members.
"We are once again calling on ScotRail to return to the talks so we can negotiate a fair deal that we can put to our members.”
A spokesperson for Mr Lindsay said the 4.2 per cent offer had not been put to members “because all pay offers go before the national executive committee first”.
The RMT union, whose ScotRail members include train conductors and ticket examiners, is due to consider the revised 4.2 per cent offer next week.
Scottish Conservatives transport spokesperson Graham Simpson said: “Once again, train passengers in Scotland are set to suffer thanks to SNP complacency and dithering.
“Yesterday I asked [transport minister] Jenny Gilruth what contingency plans were in place should Aslef reject the current pay offer and she had no answer.
“It’s clear she and the SNP Government just assumed the offer would be accepted.
“Now, it appears, we’re back to square one and the Scottish public will have to endure the woefully-inadequate reduced ScotRail timetable for even longer.
“Ministers must get ScotRail and the union back around the table immediately to end this chaos as quickly as possible.”
Scottish Labour transport spokesperson Neil Bibby said: “It’s hard to imagine this shambolic ScotRail service getting any worse, but that’s exactly what will happen if the SNP fail to resolve this situation.
“This Government’s disgraceful lack of leadership has left services in chaos and industrial relations at an all-time low.
“However much the SNP try to pass the buck, blame for this turmoil lies firmly at their door.
“Rail passengers can’t keep paying the price for SNP failure – the Government need to get round the table with the unions and ScotRail and agree a fair deal for rail workers before services grind to a halt altogether.”
Mark Ruskell, transport spokesperson for the Scottish Greens, which is in a power-sharing deal with the SNP-led Scottish Government, said: “I’d encourage ScotRail to get back round the table with Aslef and secure a mutually-acceptable resolution to these negotiations as soon as possible.”
A spokesperson for the Scottish Government’s Transport Scotland agency, which controls the newly-nationalised ScotRail, said: “We are disappointed that Aslef, having given due consideration to the terms they negotiated, have decided to reject the very good offer on the table, an offer which is in part self-funded through increased revenue and efficiencies.
"While we understand any union’s desire to obtain the best deal possible for their members, the stark realities of the financial pressures we are facing across Government are evidenced by the Spending Review published just yesterday.
"While, regrettably, this decision appears to mean further disruption for passengers in the immediate term given there is no indication that drivers will return to previous rest day working and overtime arrangements, we would encourage all parties concerned to get back round the table to resume negotiations.”
David Simpson, ScotRail Service Delivery Director, said: “We’re incredibly disappointed and frustrated that ASLEF bosses have rejected this improved pay offer. It’s astonishing that they will not even put this offer to their members.
“Our substantially improved pay offer reflects the cost-of-living challenges faced by families across the country, while balancing it against the need to provide value for the taxpayer.
“We have offered to meet ASLEF but, in the meantime, would urge them to reconsider this offer in the interest of their members and the future of the railway in Scotland.”
Meanwhile, the train operator told The Scotsman it planned to publish a temporary Sunday timetable on Thursday or Friday to give passengers more certainty, having been unable to do so previously.
Last Sunday, 320 services, or some 30 per cent of the total due to run, were cancelled with no advance notice because of a shortage of drivers.
Chief operating officer Joanne Maguire said: “We are confident that this Sunday will be improved on last Sunday.”
She pledged there would be a “resilient and reliable service” of about two-thirds of normal trains.