Govia Thameslink Railway (GTR), which runs the Southern franchise, has warned the RMT union its offer will be rescinded if strikes on Friday and Saturday go ahead as planned.
The offer, extended to the union three months ago, includes a five-year jobs guarantee, above inflation pay rises for two years, guaranteed minimum levels of overtime and more trains having a safety-trained person on board.
In a letter to RMT general secretary Mick Cash, GTR human resources director Andy Bindon said: “Your unnecessary action is continuing to have a material and negative impact on people’s work and family lives as well the regional economy and I urge you to stop.”
GTR has said it is ready to meet union representatives this week.
But a response to the letter by Mr Cash suggested the warning was unlikely to terminate the planned action.
He said: “The action later this week goes ahead due to intransigence of the GTR bosses and their cheerleaders in Government who are pulling the strings in this dispute. RMT will be holding a national rally at Parliament tomorrow lunchtime in support of the fight for safe services on Southern Rail.
“The union remains available for serious talks and we would repeat the call to Transport Secretary Chris Grayling to get out of his bunker, get hold of the Southern management and get round the table.”
The latest spat comes after the RMT confirmed it was balloting Southern drivers for further action over the extension of driver-only operation trains.
The ballot will open on Friday and close on November 18 – mirroring the timetable for action by sister union ASLEF.
A GTR spokesman said: “This ballot is unnecessary. Our proposals to transfer the full operation of the train to the driver to allow the on board supervisor to concentrate on customer service are totally safe, and a proven method of operation.