The lobbying is taking place before nominations for the kingdom’s next Prime Minister close on Tuesday.
A nominee needs to win the support of half of the 26-member Parliament to get the appointment.
So far 10 of the 17 newly elected People's Representatives have publicly identified themselves as supporting Siaosi ‘Ofakivahafolau Sovaleni – the interim Minister of Education, as their choice for PM.
The group numbers 11, including himself, and so he is almost assured a nomination.
Meanwhile, ‘Aisake Valu Eke, a former Minister of Finance who regained his Tongatapu no. 5 seat, is a spokesperson for the remaining six People's Representatives, but his group will also need to attract the Nobles' votes in order to win a simple majority in the secret ballot.