Papua's governor, Lukas Enembe, says people should wait for the official vote count in Indonesia's elections before claiming victory.
Both presidential candidates, Joko Widodo and Prabowo Subianto, have claimed election wins, but several polls back the incumbent Mr Widodo.
Official results will be released by May 22.
Mr Enembe told state news agency Antara that spreading fake news about the vote will trigger chaos and should not be allowed.
The latest polling by one observer group showed just 26,000 votes in Papua, with several districts yet to be counted.
Delays in the arrival of ballot boxes on Wednesday's one-day vote meant voting for many Papuans took place on Thursday.