Northern has previously been asked by politicians to set out an action plan to restore an acceptable level of reliability for passengers in the run-up to Christmas.
Mr Burnham said the government needed to ensure that improving rail services in the north was a top priority.
Speaking on Radio 4’s Today programme, Mr Burnham said the rail industry was dragging the north backwards and it was hitting businesses.
He said: “Last Sunday we had ‘do not travel’ notices issued for English cities between Manchester and Stoke, Manchester and Chester, that is embarrassing is it not?
“That, I think, brings the UK’s northern travel system into real disrepute and it has to to be addressed if we are going to get growth happening everywhere.”
The has asked Northern and the department for transport for a response.
Northern, which is owned by a holding company of the Department of Transport, operates across the north of England, running services in Greater Manchester, Yorkshire, Merseyside, Teesside, Tyne & Wear and Northumberland, as well as into parts of the Midlands.
