The Cook Islands opposition coalition says it legitimately voted the Henry Puna government out of office on Tuesday.
But the Finance Minister, Mark Brown, has called it a farcical exercise that could result in treason charges.
The opposition had claimed the Speaker Nikki Rattle did not follow the correct procedure in ending the session of parliament last Friday.
The MPs said this left parliament still in session and they used the opportunity to hold the no confidence vote.
RNZ International's Cook Islands correspondent, Florence Syme Buchanan, said the Queen's Representative Tom Marsters has avoided meeting the opposition group and has likely sought lawyers' advice.
"The Cook Islands Party government remains the government until such time as the Queens Representative is satisfied that the events in parliament were indeed legal and the opposition acted correctly when it attended to the order paper which included a motion of no confidence in Prime Minister Henry Puna and his cabinet."
"It will be very very likely that right now the Crown Law office is burning the midnight oil to examine our constitution possibly with the advice of Cook islands constitutional expert Alex Frame in New Zealand to see whether the events were legal or not, " she said on Tuesday night.
Cooks finance minister labels attempted ouster 'treasonous'
The Cook Islands finance minister Mark Brown said what he calls a 'stunt' by the opposition could lead to them being charged with treason.
"The activity that has taken place at parliament can be regarded as a non-event," he said.
"However, I believe that if the opposition tries to push this further they would be bordering on an act that's treasonous, because it is trying to overthrow a legitimate government through an illegal means."
He said the 13 opposition MPs may be investigated for criminal offences in relation to their actions today.
The vote was held in Parliament on Tuesday presided over by the deputy speaker of parliament, Rosy Brown -- a member of the opposition Cook Islands Party -- while several government ministers and MPs were away.
RNZ International's correspondent in Rarotonga said the opposition had been unsuccessfully seeking to see the Queen's Representative so he could confirm a change of government.
But the finance minister, Mark Brown, said the opposition's act was a farcical exercise that could become criminal if the opposition persisted.