The SEC's statement, late on Friday, came as Lloyd's prepared to appeal a federal court ruling in California, which - if it stands - would allow rebel names to sue the insurance market in the US for the first time.
This follows a ruling on Thursday in the Ninth US Circuit Court of Appeal, which reversed a lower court decision in Lloyd's favour.
"You have entities selling securities here that try to require investors to sign contracts saying that any subsequent suits have to be filed in a foreign court that's never heard of a security," SEC general counsel Richard Walker said.
"For the future, this means you can't waive the rights and protections of federal securities laws."
This weekend, there was confusion over the remarks. The SEC filed a supportive "amicus" brief on jurisdiction last year but has always ducked ruling formally that Lloyd's falls under its ambit.
It remains unclear whether Mr Walker, the SEC's top lawyer, was being protective of investors signing away their rights to sue or whether he was indicating that a wider-ranging move is on the cards.
So far, of 2,996 US names, 576 have not accepted Lloyd's Equitas reconstruction plan, which closed a week last Friday. Just 673 of 25,652 UK names are also holding out.
A Lloyd's spokesman said it was still taking legal advice on the appeal.Reuse content