Greater Manchester Mayor Andy Burnham has called for a temporary fare cut on rail routes affected by an interim timetable.
Northern has aborted about 2,000 services since new timetables started on 20 May, with more than 200 cancelled or heavily delayed on Friday.
The operator has now introduced a temporary timetable that removes 165 daily services until 29 July.
Mr Burnham said Northern tickets should also be accepted by other operators.
Govia Thameslink Railway (GTR), which runs Great Northern, Thameslink and Southern, has also introduced a reduced timetable following cancellations and delays.
A spokesman said about 160 of its 3,600 daily services have been removed from the network to make for a “more consistent timetable”.
“Many Northern passengers are already significantly out of pocket following recent disruption,” Mr Burnham said.
“Now, people who have bought advance or season tickets valid in the next two months face receiving a lower level of service than was being offered when they bought those tickets.”
Areas affected include Manchester, Liverpool, Lancashire and the Lake District line between Oxenholme and Windermere.
Commuters were still complaining of problems on Monday – with more than 100 trains cancelled or severely delayed – despite the reduced timetable.
One passenger said: “Even the emergency schedule is a struggle for you” and another spoke of Northern’s “ineptness”.
@northernassist emergency schedule in place because you cannot run a rail service. First train on that emergency schedule from Urmston. Late by 16 minutes. Even the emergency schedule is a struggle for you. @AndyBurnhamGM sort this please.
— Bearded Twits (@bearded_twits) June 4, 2018
End of Twitter post by @bearded_twits
Well done @northernassist the 1st train on the new improved timetable is late. I am truly in awe at your ineptness
— Mark Williams (@williamsmark81) June 4, 2018
End of Twitter post by @williamsmark81
@northernassist, returning to a reliable timetable, just as bad as last week, are you trying to get me fired! Since this new timeable came in I’ve not made it to work on time and you always strand me at work with no way home at the end of the day, costing me more than I earn 😡 pic.twitter.com/lHu2k9e59W
— Duncan Cathie (@DuncanCathie) June 4, 2018
End of Twitter post by @DuncanCathie
Northern’s managing director David Brown has apologised for the “very poor start” to the reduced timetable, saying: “We’ve been cancelling far too many trains, inconveniencing far too many people and we’re truly sorry for that”.
He told BBC Breakfast the timetable was more stable but “it will take two or three days to bed in”.
“It’s not acceptable, and we’re putting all our efforts into trying to fix this,” he said, adding “it’s only right” the company would be offering compensation to passengers.
The temporary timetable removes 6% of the operator’s total services until a full timetable is expected to resume at the end of July.
Transport Secretary Chris Grayling has said government-owned Network Rail, which manages the infrastructure, was “far too late in finalising planned timetable changes and this must not happen again”.
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The RMT rail union’s general secretary Mick Cash said the minister should “get out” and his members were facing public anger “without a shred of support” from Mr Grayling or Northern’s management.
Wigan MP Lisa Nandy said the transport secretary was due to meet with MPs whose constituents are affected on Monday.
Mr Burnham has repeated his calls for a “substantial offer of compensation for those with advance or season tickets”.
“In my view, if the new May timetable is not fully operational by early August, proceedings should be initiated to remove the franchise,” he added.
“As far as I am concerned, this emergency timetable represents the ‘last chance saloon’ for Northern.”
Britain’s rail timetable is updated twice a year but May’s update included more changes than normal in an attempt to improve punctuality and account for extra services and capacity following billions of pounds of investment.
The timing of all Govia Thameslink Railway and most Northern trains was changed, but all new journeys had to be individually approved by Network Rail.
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