Southern rail passengers face more strikes and fresh chaos after an offer aimed at ending the long-running dispute over conductors was rejected.

The Rail, Maritime and Transport (RMT) union described the offer as a "bribe", and disputed "bogus" figures on the number of staff working during strikes.

Southern urged the union to put its offer to a referendum to end the row over the role of conductors, saying a £2,000 lump sum is back on the table if they do.

But it was immediately rejected by the union, saying it did not move the dispute forward "a single inch".

The union is pressing ahead with a fresh round of strikes, with members due to walk out for three days from midnight on Monday.

Southern had claimed that increasing numbers of staff were turning up for work during strikes, but this was denied by the union, which said the action was being solidly supported.

RMT general secretary Mick Cash said: "There is no offer whatsoever to start engaging in serious talks about the safety and access issues at the heart of this matter.

"Instead, Southern have rehashed the £2,000 bribe to our members even though the company have been told repeatedly that money is not the issue and that the safety of passengers and staff is not for sale.

"RMT disputes the bogus figures on the number of staff working. Our reps at all locations report that morale is high and that support for the strike action remain rock solid."

Charles Horton, chief executive of Southern's owner, Govia Thameslink Railway, said: "The RMT needs to reflect on the hardship, distress and frustration being experienced by our customers and employees. Everyone wants to see an end to this dispute, but it is clear that, as things stand, there is currently little prospect of a negotiated settlement between us, however much we've tried.

"There have been significant developments since the union tabled the original ballot to conductors over six months ago. In order to move things forward, I am asking the union to let conductors - the people at the heart of this matter - determine whether this dispute comes to an end or continues.

"Nearly a third of conductors are now coming in to work on strike days and we expect that to increase. There is a full and fair offer on the table and it's time to stop the strikes and move forward."