Southern Railway has offered to hold fresh talks in a bid to avert another strike by the biggest rail union in the long-running dispute over staffing and the role of conductors.
The company said it will meet the Rail, Maritime and Transport union if it suspends industrial action.
The company suggested meeting on April 4 - the date set for the next strike by RMT members.
Charles Horton, chief executive of Southern's owners, Govia Thameslink Railway (GTR), said the talks will only go ahead if the union commits to calling off its action.
In a letter to the union's general secretary, Mick Cash, he said: "Our passengers, staff and the regional economy want certainty and an end to your industrial action, not a 24 hour truce.
"It's disappointing that the RMT are now threatening a 31st day of strike action on 4 April. Over the past year, we have met with the RMT countless times to try and settle your dispute. Unfortunately, each time has ended in disappointment."
GTR said the RMT should go further than calling off the April 4 strike and commit to ending its industrial action on Southern to enable "constructive and goodwill talks aimed at finding a negotiated solution".
Southern said it ran 90% of its normal service on each of the last two RMT strike days, adding that over half of conductors and on board supervisors staff had signed on to work.