Shadow Transport Secretary Andy McDonald insisted Mr Grayling was responsible for the chaos suffered by millions of commuters over the last two weeks, and told The Yorkshire Post he would be raising the issue in Parliament on Monday.
Mr McDonald could table an urgent question and force Mr Grayling to appear before MPs in the Commons to answer questions about the fiasco.
The Labour frontbencher also joined calls for Mr Grayling to resign over his handling of the railways, following fierce criticism from MPs and northern metro mayors such as Sheffield City Region’s Dan Jarvis and Greater Manchester’s Andy Burnham.
Passengers on Northern and Govia Thameslink services in the South have suffered daily misery since the introduction of new timetables on May 20.
Services continue to be delayed and cancelled in unprecedented numbers and disruption is expected to continue for weeks.
The Transport Secretary has so far placed most of the blame on Network Rail for being late in finalising planned timetable changes.
But Mr McDonald called on Mr Grayling to take “urgent and effective action to rectify this debacle as quickly as possible” and said he must “explain himself” to MPs when Parliament returns from recess on Monday.
The Labour frontbencher said: “We’ve been saying for weeks that he’s been asleep at the wheel on major issues.
“He’s clearly ultimately responsible for all of this, wherever the deficits lie in terms of failing to prepare for a train crew to be in the right place at the right time.
“And he seems to forget that he’s also responsible for Network Rail.
“But what he shouldn’t be doing is blaming timetablers who are working so hard trying to pull this round.
“It’s his responsibility for all of this and it’s just characteristic of his attitude to all of these difficulties that the railway industry is facing by blaming other people rather than looking in the mirror.
“If he had any decency he would step down, I don’t expect that to happen, but I will be challenging him on Monday when Parliament returns because this simply cannot go on.”
Mr Grayling and Rail Minister Jo Johnson have offered private talks with affected MPs on Monday evening.
Northern rail has announced a temporary timetable change to help reduce last minute cancellations.
From Monday, 6 per cent of its daily train services will be temporarily removed until the end of July.
The move affects the Lakes Line, Blackpool, Lancashire, Manchester and the Liverpool City Region.