SODELPA held the balance of power with the FijiFirst government and the People's Alliance-National Federation Party coalition both commanding 26 seats in Fiji's expanded 55-member parliament.
SODELPA narrowly sided with the coalition 16 votes to 14 after days of negotiations, but its management board will meet again on Friday after some members whose terms had expired were part of the Tuesday meeting.
The board will decide whether the decision to join the coalition stands or whether the vote needs to be held again.
Political turmoil continues in the nation marred by coups, with the incumbent nationalist government refusing to concede the election.
Prime Minister Frank Bainimarama, Attorney-General Aiyaz Sayed-Khaiyum and Police Commissioner Sitiveni Qiliho cited incidents of stonings against Indo-Fijians as a rationale to request army intervention in maintaining law and order.
Little detail has been given about the purported racial targeting.
But prime minister-elect and People's Alliance leader Sitiveni Rabuka took to Twitter to say senior police officials confirmed to him the stone-throwing accusations had been made up.
He branded Sayed-Khaiyum an anarchist for trying to trump up racial divisions.
"(Sayed-Khaiyum) is trying to set the nation alight along racial lines by claiming that racially motivated acts are occurring in Ba," he wrote in a Friday morning post.
"He is lying."
Both sides have called for calm.
Fiji's assistant police commissioner has also resigned after the army was called in to maintain law and order following political uncertainty.
The Fijian Police Force confirmed Abdul Khan's departure in a Friday morning statement but said it was due to personal reasons after local journalists cited sources saying it was because he disagreed with the decision to bring in the army.
Indo-Fijians are using the hashtag FijiIsUnited, writing on social media, "I fall in the minority group in Fiji and I have felt completely safe in the lead up to elections, during elections and post-elections".
Tensions between Indigenous Fijians - about 60 per cent of the population - and Indo-Fijians - the descendants of indentured Indian labourers who make up about one-third -have marred politics.
Rabuka, who first took power through a 1987 coup and was prime minister through the 90s after a democratic election in 1992, put in place a constitution branded racist for favouring Indigenous Fijians.
A new constitution was put in place after Bainimarama took power, also through a coup, and removed a race-based electoral system that favoured Indigenous Fijians.
Bainimarama said the 1997 constitution had caused racial discrimination.
