New Zealand secured the top place in their pool on day two of the tournament by beating South Africa 12-7 and Ireland 26-7.
Argentina qualified with a 17-7 win over Canada, 26-19 over Samoa and a 19-26 loss to Fiji.
Tied 7-7 at halftime after a third-minute try to Leroy Carter, to which South Africa responded just before halftime with a try to Mfundo Ndhlovu, New Zealand claimed the win when Cody Vai scored in the 10th minute.
Against Ireland, New Zealand scored first through Brady Rush after five minutes. Ireland replied after seven minutes when Chay Mullins scored. However, before the break, Ngarohi McGarvey-Black crossed for the All Blacks Sevens to take a 14-7 lead to the break.
But, in the second half, after sterling Irish efforts tries to Carter two minutes from the end and another to Fehi Fineanganofo secured the win.
Should New Zealand qualify for the semifinals, they will start at 7.29 pm, with the final scheduled for 12.15 am on Monday.
New Zealand's Black Ferns Sevens have their first fifth consecutive Cup title in a season in their sights in Hong Kong and face a semifinal against Fiji at 7.06 pm on Sunday.
Fiji gained their place with wins over Ireland 17-7, Brazil 36-5 and the United States 19-14, while their only loss in pool play was 5-35 to Australia.
In the Black Ferns' first game on day two, they routed Canada 46-0 and then repeated the effort in their quarterfinal against the same side 45-14.
In their pool game, Shiray Kaka and Portia Woodman-Wickliffe scored two tries each, with Michaela Blyde, Kelly Brazier, Alena Saili and Stacey Waaka also scoring.
Then, in their quarterfinal, Jorja Miller and Risi Pouri-Lane scored two times each, with Blyde, Brazier and Saili scoring. Tyla Nathan-Wong converted five of the tries.
The women's final will be played at 11.40 pm.