Southern rail owners Govia Thameslink Railway on Tuesday accepted the offer of face-to-face talks between its chief executive, Charles Horton, with the RMT general secretary, Mick Cash. Photograph: Andy Rain/EPA

The first face-to-face talks between the boss of Southern Rail and the leader of the RMT union are to be held on Wednesday in an attempt to resolve the six-month-long dispute.

Conductors on Southern will be on the second day of three consecutive days of action, with a further four 72-hour strikes planned over the autumn. Southern intends to run just more than 60% of its normal timetable.

Despite having mounted legal challenges to the strike and ruled out further talks, the owners of the troubled franchise, Govia Thameslink Railway, on Tuesday accepted the offer of face-to-face talks between its chief executive, Charles Horton, and the RMT general secretary Mick Cash.

However, the prospect of a resolution appears slim. Cash said he believed Horton had altered his position over guarantees of a second staff member on every train – a sticking point in the dispute – but the company said the RMT was deliberately distorting Horton’s comments, made in a BBC radio interview on Tuesday morning. Horton also asked the RMT to call off this week’s strike to show serious intent and allow productive talks to take place, but Cash later confirmed the strike would remain on.

In his written response to Cash, Horton added that the company was pressing ahead with changing the role of conductors to onboard supervisor. He said: “It would be beneficial to everyone if we can do so with the agreement of the RMT, but this has to be on the basis of the principles we have made clear to them throughout. Our proposals remain unchanged from 8 August when we set out our full, fair and comprehensive eight-point offer, on top of previous assurances made to you.”

The first day of the current strike action on Tuesday saw passengers suffer fresh disruption as overrunning engineering works on the Brighton mainline compounded problems, leaving rush-hour trains from the south coast cancelled or delayed by up to an hour. Network Rail apologised for a breakdown that meant the railway between Gatwick and Brighton only reopened to trains at 7.20am.

Ministers condemned the RMT. Paul Maynard, the rail minister, said: “It is disappointing that passengers once again face needless and unjustified strike action by the RMT, after the union advised its members to accept the new roles being offered by the operator. The union leaders have continually rejected a deal that protects jobs and ensures that conductors will carry on delivering safe, accessible and more reliable rail services.”

A commuters’ group has raised concerns with the government about the health and safety of rail passengers on Southern. The Association of British Commuters wrote to the Department for Transport on Tuesday, warning that passenger safety was jeopardised. A spokesman said: “Passengers are having to cope with absolute chaos now. On any day, trains are overcrowded or cancelled and the situation is dangerous.”