The news organisations said in a motion filed on Tuesday in Miami-Dade County court that the 19-year-old pop singer has no legal basis to prevent their release.
Nine videos were made at the Miami Beach police station after Bieber was booked on January 23. One was previously released.
Bieber's lawyers have asked a judge to allow them to review the other videos before their potential release.
A hearing is scheduled for Thursday.
Bieber has pleaded not guilty to misdemeanour charges of DUI, resisting arrest and driving with an expired licence. Police say he and singer Khalil Amir Sharieff were involved in an illegal street drag race in Miami Beach.
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