One journalist said the music industry was "making mischief" to get more money from sites such as YouTube.
Figures from the Recording Industry Association of America RIAA show that CD sales in the US fell from $13bn £9bn in 1999, to $1.5bn in 2015.
It has been published at a time when the US congress is evaluating the DMCA, and record labels are renegotiating deals with YouTube.
The DMCA has a so-called "safe harbour" provision that stops websites being held responsible for copyright infringement by their users.
Critics of the open letter have highlighted the fact that some websites already offer tools that can automatically detect copyright infringement.
Facebook has said it is developing its own content detection tools, which are currently available to selected media partners - and there are third party tools such as Kobalt, which record labels can use to trawl social media sites and detect copyright music.