The Cook islands prime minister, Robert Woonton, says while he intends to serve a full term in office, he cannot rule out an early election.
Mr Woonton says a by-election is scheduled for next month for the only seat vacant at this time.
And he says due process has to be followed over claims that two other MPs are no longer eligible to stay in parliament.
The prime minister says he is baffled by the reported resignation of MP Teina Bishop.
Dr Woonton says Mr Bishop has not actually submitted his resignation to parliament's speaker
"Teina Bishop is a question that is baffling not only government members. His leader Sir Geoffrey Henry, he is baffled by his stated intention of resigning. If one resigns from parliament you hand your resignation to the Speaker of the House, not your leader. The leader of the opposition does not declare a seat vacant."