Joe Natuman and the Prime Minister Sato Kilman have been meeting all weekend to try and resolve the impasse, which began after 14 government MPs were last month jailed for bribery.
On Friday, the country's highest court rejected their appeals, which means the 14 are now no longer MPs.
Kilman has rejected the opposition's proposal to form a government of national unity, instead saying he'd rather the President Baldwin Lonsdale dissolve parliament, which he threatened to do if an agreement was not reached by Sunday.