One of the Union of Moderate Parties' six MPs, Tanna MP Robin Kapapa, recently formally defected to the opposition from the Bob Loughman-led government.
The party's non-parliamentary membership is urging the rest of their MPs to follow suit.
The UMP president, former prime minister Serge Vohor, called for a meeting of the party's national executive today to discuss a possible move by all its MPs
However while Vohor reportedly wants the UMP to defect, the party's parliamentary leader, deputy prime minister Ishmael Kalsakau, is opposed to the idea.
Earlier, the Secretary General of the UMP, Wendy Himford, said the UMP's Tanna regional members want their MPs to join the opposition.
The Daily Post reports Himford saying the party's Tanna executive moved a resolution for fellow UMP Tanna MP Nakou Natuman to join Kapapa in defecting.
Kapapa was the second MP this month to announce he was leaving the coalition government, following Torres MP Christophe Emelee.
The two defections meant the Ralph Regenvanu-led opposition appeared to have 24 MPs in the 52-seat parliament.