The Scottish Government said it would consider plans outlined yesterday for a new system backed by Royal Charter.
First Minister Alex Salmond last year called for a specific Scottish solution to press abuses. But a spokesman for the Scottish Government said the new proposals would be considered as part of the deliberations of its expert group looking at the findings of the Leveson inquiry.
Proposals for a Royal Charter were given a cautious welcome by the LibDems, who said it was up to their Coalition colleagues to prove it could work.
However, Labour warned they could be manipulated by politicians. The plans were condemned by the campaign group Hacked Off, which called them a "surrender to press pressure".
The Conservative plans would result in a Royal Charter overseeing a new press watchdog.
The charter could only be reformed with the support of at least two-thirds of MPs.
Bob Satchwell, executive director of the Society of Editors, said it was studying the proposals.
He added: "To suggest this is a surrender to press pressure simply shows there are those who seem intent on neutering all of the papers."