The competition was washed out due to rain.
Cook Islands Cricket Association chief executive officer Davis Teinaki said the matches would not be played on a later day.
“These matches were not postponed so the teams that were scheduled to play will receive two points each,” Teinaki said.
“The weekly league will now resume on September 17 after the Hamilton team’s Rarotonga tour.”
Nine clubs in the men’s division and seven in the women’s will be competing in the Twenty20 format competition.
The Arorangi men’s and women’s team have pulled out of this year’s competition due to a lack of players.
In round one, defending men’s champions Turangi was scheduled to host Avana, while Matavera was supposed to take on Tupapa. Takuvaine was to play Tupapa II and Nikao to battle Titikaveka in the other men’s matches.
Defending champions Muri, which was supposed to play Arorangi, was on a bye.
In the women’s competition, Matavera was scheduled to battle Nikao, Turangi to face Avana and Takuvaine to play Tupapa.
Teinaki hopes the break will give teams time to prepare well before the season proper begins in a fortnight.
Meanwhile, the Hamilton-based Northern District women’s cricket team will arrive in the country on Thursday.
The team will play a match each against the national women’s side, Avana and Turangi clubs.
Teinaki hopes the upcoming matches will be a good test for the local female players playing in the domestic competition.