This came after Tu'ilakepa announced six bills the government is trying to push through under urgency would first have to go to the House's Standing Committee on Legislation.
Matangi Tonga reported that Prime Minister 'Akilisi Pohiva had not explained why the bills are urgent.
The threat of impeachment is the latest wrangle in a legislature that has faced a series of walkouts by the opposition in the past week.
It also comes as King Tupou VI has been presented with a series of petitions that seek to have parliament dissolved.
The website reported Tu'ilakepa responded to Mr Tapueluelu's threat by saying "you take legal action if you want to".