But the train company has offered to hold fresh talks aimed at resolving the bitter dispute over the role of conductors.
Charles Horton, the chief executive of Southern’s owners, Govia Thameslink Railway, has written to the leader of the Rail, Maritime and Transport (RMT) union saying he will meet him today.
The move followed disruption to services caused by a strike which is due to continue until midnight tomorrow.
Passengers faced long delays with many tweeting their frustration on Twitter.
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Mr Horton urged the union to call off this week’s strike and allow ‘productive’ talks to take place.
He told RMT general secretary Mick Cash: ‘I’m prepared to free my diary to meet and to show your serious intent, I would like the RMT to call off the rest of the strike action planned for this week.
‘Everyone – the travelling public, our staff and the regional economy – have faced months of misery and disruption.’
Conductors working for the company are protesting over a safety dispute, with 14 days of strike action planned up until Christmas.