A spokesman for Mr Khan said the mayor will “work closely with a Labour government to deliver a system that provides the service passengers deserve”.
However, the spokesman added: “The existing commuter rail lines in London are clearly not fit for purpose, with cancellations, delays and poor reliability.”
It comes after Mr Khan had hoped to run trains currently operated by Southeastern and Great Northern, which link towns across the commuter belt to stations in central London.
His proposals had represented a diluted version of a plan mooted by Boris Johnson during his time as mayor, as he has sought to extend TfL’s network across the home counties.
As for Labour’s GBR plan, this will not encroach upon Mr Khan’s TfL operations – which include the London Underground, Docklands Light Railway, London Overground and Elizabeth Line.
The latter two networks include trains operating as far as Watford and Reading.
A source close to the situation said TfL and the mayor’s office would continue to press a Labour government for the right to run more routes, especially those mostly within Greater London.