Management and workers at Irish Ferries today attended separate exploratory talks at the Labour Relations Commission to try to resolve the escalating row.
At least 650 of the company's 1,200 strong workforce have been removed from the payroll in the dispute over the outsourcing of employment on its MV Normandy service between Rosslare and France.
As the ships' officers strike entered its fourth day, delegations from SIPTU and the management met the LRC facilitator separately.
Before the meeting Mr Paul Smyth, SIPTU branch secretary, said: "I am going in to see if we can resolve the substantial issue and I'm hopeful.
"It is more difficult now with people on strike. But it won't be the first time that we have solved a difficult problem. I'm always hopeful if talks are taking place."
He said that management at Irish Ferries had no interest in meeting with them up until this point. Mr Smyth said if the company started to attempt to set conditions for the talks it would not work.
But the company says SIPTU was in breach of agreements and that it was up to the ships' captains when they wanted to return to work.