Strikes by Southern Railway workers set for Thursday and Friday will be suspended if the company agrees to urgent talks without pre-conditions, the union at the centre of the dispute has offered.
Members of the Rail, Maritime and Transport union are taking industrial action for the third consecutive day and are due to stay out until the weekend.
Hundreds of thousands of rail passengers are suffering disruption because of the strike, with hundreds of trains cancelled and some stations having no services at all.
RMT general secretary Mick Cash said Southern's owners Govia Thameslink Railway had set out a series of pre-conditions in a letter to the union.
"The company knows that prescriptive pre-conditions would not allow genuine talks to take place.
"In an effort to break the deadlock and get the talks process moving RMT is prepared to suspend strike action set for Thursday and Friday if Southern agree to urgent talks without pre-conditions.
"The ball is now in their court," he said.
The union has staged a protest outside the Transport Department in London, accusing the Government of "sabotaging " attempts to reach a deal.
A Southern spokesman said: "We have made the RMT a fair and comprehensive eight-point offer, and we'll meet them any time, any place, anywhere to talk about our offer on our network to settle this dispute.
"This strike has to stop and has to stop now."
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