Conservatives have dismissed Labour plans for a Leveson law as lacking in detail as they prepare to produce the Government's draft Bill on press reform.
The Leveson Inquiry has not led to cross-party agreement on press regulation
The party's six-clause Bill, which it says also enshrines freedom of the press into law, will be considered at cross-party talks on Thursday, according to Tory sources.
But the government's own attempt at drafting legislation, which Conservatives said would show a law was unworkable, will also be produced in time for the meeting.
In the hours after the Leveson inquiry report was published Labour leader Ed Miliband said he believed the proposals should be "accepted in their entirety" but the draft Bill drops support for involving broadcasting regulator Ofcom in any new system.
A Tory source said: "This new draft Bill completely rejects the involvement of Ofcom. They have gone from accepting the report in full to rejecting one of the major recommendations.
"We will look at the proposals at the cross-party talks. We are going to make sure (the government draft Bill) is ready for then.
"Not only have they u-turned, even they admit that their proposals are quite top line and don't address the details."
Labour's draft legislation calls for the Lord Chief Justice to head up a panel that decides if a new press watchdog is up to scratch. The group would recognise a self-regulatory body, which would then become a press standards trust, if it meets certain requirements, including being demonstrably independent of newspapers.
The new body would set a binding code of standards and would run an arbitration scheme to deal with civil complaints.
After two years, the recognition panel would carry out checks to ensure the new regulator is carrying out its work rigorously, followed by an assessment every three years after that.
The proposals would set in law major incentives to join the trust, including lower levels of high court damages and costs.
Ms Harman said: "This Bill puts into effect the central recommendation of Lord Justice Leveson's report - legal backing for the new system of independent self-regulation by the press. The Bill would ensure that the system was verified at the outset and given a health check once every three years.
"This Bill is an offer to MPs on all sides of the House who want to implement Leveson's proposals. It shows that a Bill can be done in a way that is not cumbersome or invasive, and we look forward to discussing it in the cross-party talks on Thursday."
Deputy prime minister Nick Clegg discussed the proposals with Mr Miliband by telephone last week.
A senior Lib Dem source said: "The Liberal Democrats welcome the publication of Labour's Bill as an important contribution to the cross-party talks.
"Although there is more work to be done to ensure that legislation is proportionate and workable it demonstrates that it should be possible to achieve this goal.
"The focus of the Liberal Democrats will be to work to further improve the Bill to make it very difficult to amend in the future.
"Liberal Democrats look forward to discussing this Bill with all parties alongside the draft that the Government is currently working on."
Ms Harman told BBC Radio 4's World At One: "I'm disappointed they have dismissed the Bill because we have asked for it to be on the agenda for the cross-party talks that Maria Miller is chairing on Thursday.
"It's not so short that it wouldn't have legal effect. It's properly drafted, it would have exactly the effect that Lord Justice Leveson put forward. I think it is disappointing for the government to be rejecting it out of hand."
Ms Harman said Lord Justice Leveson's call for Ofcom to be the organisation which formally recognised a new watchdog was a preference, not a "firm proposal".
"We said we agree with Lord (Justice) Leveson, yes, Ofcom would be fine, but in the debate last Monday a number of MPs said that they weren't happy with Ofcom and they gave a number of reasons. This is not a central principle."
Prime minister David Cameron said it would not be "the end of the world" if Leveson's proposals for statutory under-pinning went ahead, but made clear he would still prefer the creation of a self-regulatory system without the need for legislation.
Mr Cameron told reporters at a Westminster lunch: "I think the press needs to have a proper regulatory body, where people feel if they complain they will get proper redress. We have that in other walks of life, I believe we should have that for the press.
"I think the Leveson proposals for what an independent self-regulatory system should look like are pretty good - up to £1 million fines, prominent apologies, that's what needs to be put in place.
"What is good news is that the press themselves, the editors, have come together and - as I understand it - pretty much signed up to that and said 'we are prepared to put in place Leveson-compliant self-regulation'.
"The choice for politicians and the country is do we want to back that with statutory under-pinning or do we think we can find another way of doing it? My argument is that we can find another way of doing it.
"Let's be clear, the Leveson statutory under-pinning isn't the end of the world. The world doesn't end tomorrow if we have statutory under-pinning.
"But I found, as I looked hard at this argument over the summer and autumn, that once you start drafting a law which has a statutory under-pinning, you find you have created a Press Bill. It may not have that much that is actually frightening in it, but it becomes a very easily amendable piece of work, which is why we should try to avoid it. I think we can avoid it."
Mr Cameron added: "Proper, independently verified, tough and strong self-regulation with proper redress for victims, proper apologies, proper fines - that is what we should get and what the public want.
"The public want to know `If the press screw up and get it wrong on me, fines and apologies (will follow)'. That's where it is at. I think if we crack that, we have got the whole thing sorted."