A Nauru MP allied with the President Sprent Dabwido says the new Speaker, Godfrey Thoma, is acting unconstitutionally in not dissolving Parliament.
Baron Waqa says this refusal has prompted his group to boycott the last two sessions of the legislature.
The boycotts meant the parliament lacked a quorum and so could not undertake any work.
Mr Thoma says there cannot be a dissolution until MPs have debated the President's advice that Parliament be dissolved.
But Mr Waqa says to negate this advice the President and his ministers would have to be voted out and this has not happened, so the Speaker's actions are unconstitutional.
"In this case Parliament wasn't able to resolve anything. It couldn't remove the President and his Ministers. After the 7th day, according to our constitution then the House will have to be dissolved by the Speaker and it clearly states that the Speaker is bound by the Constitution to dissolve the House."
He says he hopes that a new election can go ahead within weeks.