District Attorney Martha Coakley said she and the alleged victim at the center of the case "agree that our time is better spent preparing for trial" on Jan. 18.
Acting on a request from prosecutors, a judge last week issued an order barring the media from identifying Shanley's accusers. Prosecutors said they feared continuing to name the alleged victims would make them unwilling to testify.
The Associated Press, the Boston Herald, and The Boston Globe challenged the order, and on Friday Judge Stephen Neel overturned it, agreeing it was unconstitutional.
But Neel stayed the order until Monday afternoon to give the district attorney time to decide whether to appeal.
In the three years since Shanley was arrested, two of the alleged victims have spoken publicly about the case and were routinely identified in news reports. A third alleged victim has been identified occasionally. The fourth was never named.
The AP has a policy of not identifying rape victims without their consent.
Judge Charles Spurlock, who issued the initial order, cited a state law dating to the 1980s that says it is unlawful to "publish, disseminate or otherwise disclose the name of any individual identified as an alleged victim" of rape or attempted rape.
By: (AP) Prosecutors said Monday they will not appeal a judge's ruling that freed the media to identify alleged victims in the child rape case against defrocked priest Paul Shanley.