Eight acrobats plummeted up to 40ft when the scaffolding structure holding them collapsed.
The performers, from the US, Brazil, Bulgaria and Ukraine, were in the middle of a hair-hanging high-wire act.
Authorities continue to investigate the cause of the accident.
Acrobats Dayana Costa, Julissa Segrera and Stefany Neves remain in critical condition at Rhode Island Hospital, a spokeswoman told the Associated Press news agency.
Viktoriya Medeiros and Viktorila Liakhova have been listed in serious condition, while performers Samantha Pitard, Svitlana Balanicheva and Widny Nevas are now considered in good condition.
The names and conditions of three other people hurt were not released.
“The injuries fortunately don’t appear to be life-threatening,” Nicole Feld, executive vice-president of Ringling Bros. and Barnum & Bailey parent company Feld Entertainment, told a local television station.
“A lot of them were awake, talking, communicating with us.”
The collapse occurred during an act in which the eight performers hanged from their hair “like a human chandelier”, according to the circus.
According to the circus website, the eight performers, known as “hairialists”, feature in a “larger-than-life act… spinning, hanging from hoops, and rolling down wrapped silks all while being suspended 35ft in the air by their hair alone”.
The metal frame from which the acrobats hung is said to have come free from a metal truss, a circus spokesman told US media.
Further performances were cancelled on Sunday and Monday as the circus worked with federal and local officials.
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