Protesting seamen threatened to go ahead with a 48-hour strike planned for Tuesday and Wednesday after a meeting with the government failed to reach a compromise on Sunday.
The Panhellenic Seamen's Federation (PNO) said it would reconsider only if the government came back with an improved proposal.
Development Minister Anna Diamantopoulou, who represented the government in last-ditch negotiations to avert the strike on Sunday, blamed Communist party-affiliated unionists for the deadlock.
She said strike action was “unjustified,” adding that the government would do everything to protect the general interest.
The strike is expected to seriously disrupt the travel plans of thousands of Greeks wishing to go away for Orthodox Easter, which falls on April 15.
Speaking to Skai on Monday, Administrative Reform Minister Dimitris Reppas did not rule out issuing a civil mobilization order to force the seamen back to work.
The unions are opposed to the incorporation of their social insurance fund into the new national health body, the National Organization for the Provision of Health Services (EOPYY).
PNO representatives were expected to meet with Health Minister Andreas Loverdos at 3 p.m. on Monday.