The National Music Publishers' Association (NMPA) is seeking more than $250m (£197.7m) in damages.
In a lawsuit filed at the Federal District Court in Nashville, the NMPA claimed Twitter "permits and encourages infringement" for profit.
It says the situation has not improved since Elon Musk bought the company.
The NMPA, which represents firms - including Sony Music Publishing, BMG Rights Management and Universal Music Publishing Group - alleged that Twitter continues to "reap huge profits from the availability of unlicensed music without paying the necessary licensing fees for it".
It added that the infringements have given Twitter an "unfair advantage" over competitors - including TikTok, Facebook, Instagram, YouTube and Snapchat - which pay for music licences.
Twitter "stands alone as the largest social media platform that has completely refused to license the millions of songs on its service," NMPA President David Israelite said in a statement.
Twitter did not directly respond to a BBC request for comment.
Mr Musk, who recently reclaimed the title of the world's richest person, bought Twitter last year for $44bn.
The NMPA also said: "Twitter's change in ownership in October 2022 has not led to improvements in how it acts with respect to copyright."
"On the contrary, Twitter's internal affairs regarding matters pertinent to this case are in disarray," it added.
NMPA cited Twitter's downsizing of "critical departments involved with content review and policing terms of service violations", and the resignations of trust and safety chiefs Yoel Roth and Ella Irwin.
The NMPA also alleged that Twitter "routinely ignores known repeat infringers and known infringements".
Earlier this month, Linda Yaccarino, the former head of advertising at media giant NBCUniversal, became the new boss of the troubled social media firm.
Ms Yaccarino oversees business operations at the platform, which has been struggling to make money.