Vanuatu's National Workers Union says the Prime Minister has expressed dissatisfaction with the way 26 staff were laid off at Air Vanuatu.
The Union's general-secretary Ephraim Kalsakau met Mr Lini last Friday to discuss the union's concerns over the sackings, and workers rights.
Mr Kalsakau says the Prime Minister has a good understanding of their dispute with Air Vanuatu management.
"He felt that the decision by Air Vanuatu management was done in a manner that wasn't really in the interests of good industrial relations. He also felt that the reasons given for the sackings weren't really what was being said publicly."
Ephraim Kalsakau says the Prime Minister says he will talk to senior ministers and fellow Air Vanuatu shareholders to try and forge a solution, and will report back to the union by Wednesday.
Mr Lini has indicated that if he cannot affect some resolution to the case, he will not stand in the way of union plans for a street demonstration.