Mick Lynch has said industrial action will need to continue beyond May unless a reasonable offer is made to the RMT.
Britain faces the most disruptive rail strikes yet this week, with five consecutive days of action set to leave passengers stranded.
Speaking from a picket line at Euston station in London, the union leader told the PA news agency: “They (the strikes) are likely to go ahead if there’s no offer that we can work on.
“We would like to get into a situation where we’re negotiating constantly with the companies and where we didn’t have to have strike action, and then work up a settlement that our members could vote on and accept.
“But if we don’t get that there will have to be more action, and we’ve got a mandate that runs through to May this year, and if we have to go further, that’s what we’ll need to do. We don’t want that, though.”