New Zealand's Black Ferns Sevens will play England at 9.56pm on Sunday and the All Blacks Sevens will play Scotland at 11.24pm.
It was a tough day for the Black Ferns. They only beat Fiji 12-10 in their second pool game and were held to 12-0 by Russia in their third game.
New Zealand were guilty of handling errors in the face of Fiji's physical approach. But at the same time Fiji failed to take chances on offer and were not helped when Asinate Savu was sin-binned for a late tackle just before halftime.
Fiji scored first through Viniana Riwai after three minutes before New Zealand responded with tries in quick succession to Gayle Broughton, who scored in first half injury time after Savu's sin-binning, and Stacey Waaka. Savu scored a second for Fiji but the conversion missed and New Zealand held on for the win.
Again, it was a minute into the second half before the Black Ferns could make any impact against Russia. Alena Saili scored in the ninth minute and Broughton three minutes later.
England qualified for the quarter finals when scoring a 36-7 win over Ireland.
The All Blacks Sevens were untroubled in their second game of the tournament to beat Canada 33-5 with Dylan Collier, Scott Curry, Tim Mikkelson, Regan Ware and Sam Dickson all crossing for tries. However, a string of penalties awarded against them did frustrate New Zealand in the second half.
Argentina proved a tougher nut to crack in their final pool game after the sides were level at 7-7 at the break, Joe Webber having scored for New Zealand and Matias Osadczuk crossing for Argentina.
But Webber got over for a second try soon after the restart with Andrew Knewstubb crossing a minute later. Argentina pulled back the margin with a late try to 349-game veteran and captain Gaston Revol.
In other quarter finals South Africa will play Kenya, Ireland will play Fiji while France will play Argentina.