In the territorial assembly, Mr Fritch of the Tapura Huiraatira received the backing of 39 of the 57 members.
He defeated the challenges of Geffry Salmon of the Tahoeraa Huiraatira Party and of the five-time president Oscar Temaru of the pro-independence Tavini Huiraatira Party.
In a surprise development, an as yet unidentified Tahoeraa member also voted for Mr Fritch.
Mr Salmon received ten votes although his party has 11 members while Mr Temaru got eight votes.
