Thousands of commuters face a week of travel chaos, with three days of strikes planned across five rail operators.
Mr Grayling's department described the dispute with Northern as one "between a private company and the RMT", but added: "The Transport Secretary recognises the disruption caused to passengers and has met with union leaders to help bring an end to the strikes".
RMT general secretary Mick Cash said: "Every single effort that RMT has made to reach negotiated settlements in these separate disputes with the different train operating companies over safe operation and safe staffing has been kicked back in our faces and we are left with no option but to press ahead with the action".
Northern says it will attempt to operate more than 60 per cent of scheduled services between 0700 and 1900 on strike days and advises passengers that trains will be busier than usual as a result.
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All the affected firms said they would be running services during the strikes but passengers could still expect significant disruptions.
Greater Anglia said it planned to run a normal service with no alterations.
Meanwhile, South Western Railway has released a revised timetable, with some services being replaced by buses.
The shadow transport secretary, Andy McDonald, called for Grayling to take up the proposal for a summit.
"With goodwill on all sides we can reach an agreement in England as well", he added.
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A Department for Transport spokesman responded by saying that the dispute was "between a private company and the RMT".
"Employees have been guaranteed jobs and salaries for several years", the spokesman said.
The operator, which carries more than 300,000 passengers a day on 1,700 services - including many to and from Waterloo in the capital, said it would lengthen some trains and rail replacement bus services would be put on for some routes. We will operate more and longer trains than on the previous weekday strikes called by the RMT.
Speaking to the BBC's Andrew Marr Show, she said: "A lot of people rely on our railways - we want to see good service on our railways but that does mean that investment is needed".
It comes as Prime Minister Theresa May defended the latest train fare increases - of 3.4% - insisting rail investment was needed.
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