According to RNZI, the group's leaders said there was a criteria issue with the West Papuans' application, and the group's secretariat needed to establish guidelines for membership.
They said a decision would now be made when they next meet in September.
The ULMWP, an umbrella organisation of independence groups, currently had observer status within the regional body, but sought full membership.
Indonesia, which considered the movement a separatist group with no legitimacy, has associate status within the MSG.
The announcement was brought forward a day because Fiji's prime minister, Frank Bainimarama, had to leave the country on Thursday night.
From L to R; Secretary to MSG Chair, Rence Sore, Legal Adviser to the MSG Secretariat, Ilan Kiloe, MSG Secretariat Director-General, Amena Yauvoli, MSG Chair, Prime Minister Manasseh Sogavare and Secretary to the Prime Minister, Joesph Waleanisia. Photo: Solomon Islands Government