Leading the charge was Connecticut's top prosecutor, Richard Blumenthal, reports CBS News correspondent Kelly Wallace,.
"No question, absolutely none, that Craigslist is operating an online brothel here," Blumenthal said. "We're going after them to persuade them they ought to do the right thing, cooperate and eliminate the ads."
South Carolina's Attorney General Henry McMaster went further - remove all prostitution ads and pornography or Craigslist executives themselves will be prosecuted.
"It is nothing but filth," McMaster said. "It is advertisement for prostitution, it is ugly, it is harmful."
Can Craigslist be held criminally liable or sued for having illegal ads on its site? Not under current federal law, which grants immunity to sites like Craigslist for posting content it didn't create.
"Congress' rationale, which I think was a good one, that we want to not make illegal content legal or somehow inexcusable but place the onus on the people who are behaving badly in the first place," said Matt Zimmerman, a senior staff attorney with the Electronic Frontier Foundation.
The pressure on the classified online ad site, which gets 30 million postings a month, has grown in recent weeks afterwas accused of robbing two women, and killing another, all of whom he met on Craigslist, and a New York radio reporter was killed by a teenager who allegedly responded to a Craigslist advertisement.
In a statement, Craigslist's CEO Jim Buckmaster said Tuesday's meeting was productive and added, "We're optimistic that our shared concerns can be addressed … without compromising the quintessentially American values of free speech embodied in our constitution."
In November, Craigslist, at the urging of the states attorneys general, agreed to begin requiring a working phone number, a credit card and a $5 fee for anyone using the erotic services section.
Blumenthal said the action hasn't gone far enough, and said that if Craigslist doesn't respond positively in days, not months, the states' prosecutors will consider trying to change the law, or finding another route to legal action against the site.