Biles was penalised on both floor and vault as her team finished on 170.526, behind the leaders’ mark of 171.629.
With one group of athletes still to go, Biles remains in a qualifying place for each of the five individual finals.
Great Britain are in fifth place with Jessica Gadirova on target for the floor final.
Gadirova and her 16-year-old twin Jennifer are also set to finish in the top 24 and qualify for the all-around final.
But all eyes were on the 24-year-old Biles, the most successful US gymnast of all time and winner of four golds and a bronze in Rio.
She opened her qualifying campaign on the floor with her usual exciting brand of tumbling, but she bounced right out of the competition area at one point and will need to manage that in the final.
Biles was deducted 0.3 points and her score of 14.133 leaves her behind Italian veteran Vanessa Ferrari, who, at 30, is competing in her fourth Games and scored 14.166.
Biles’s 15.183 on the vault puts her in top spot on the apparatus behind team-mate Jade Carey (15.166), but in both the bars, arguably her weakest event, and the beam, she scored lower than compatriot Suni Lee.
However, her overall tally of 57.131 puts her clear in the all-around standings ahead of Lee, who has 57.166.
