Nauru remains without a speaker and a president following yesterday's session in parliament.
The clerk of parliament, Freddie Cain, says none of the MPs' put their names forward to be nominated for speaker, a position which must be filled before the president is elected.
Mr Cain says some MPs are now saying that parliament needs to be dissolved and fresh elections held, if the deadlock between the factions can't be broken.
"Three different groups and I think the bottom line is I think they want to form a government, a goverment in their own right, but they can't because nobody has the numbers."
Mr Cain says another session will be held on Thursday in an attempt to elect a speaker.
He says the caretaker government and caretaker president, Derog Gioura, will continue operating until the situation is resolved.