A number of national newspapers are taking "high-level legal advice" about whether to co-operate with a new press watchdog established by royal charter and backed by legislation.
The publishers of the Daily Mail, the Sun, the Times, the Telegraph, the Daily Star and the Daily Express said they would wait to make a decision.
They complain they were not represented in a meeting at which the three main political parties struck a deal.
Press reform campaigners were there.
A joint statement signed by Associated Newspapers, News International, the Telegraph Media group and Northern & Shell said: "No representative of the newspaper and magazine industry had any involvement in, or indeed any knowledge of, the cross-party talks on press regulation that took place on Sunday night."
It also said there were "several deeply contentious issues" about the recognition criteria which sets out what kind of publications were covered by the regulator.
Free press principle
Meanwhile, Guardian editor Alan Rusbridger said he welcomed the agreement but had "reservations" about part of the plan.
The new regulatory regime will replace the current system, under which the press is self-regulated voluntarily through the Press Complaints Commission.
The deal follows Lord Justice Leveson's inquiry into press ethics - called in the wake of the phone-hacking scandal.
The inquiry found that journalists had hacked thousands of phones, and called for a new independent press watchdog, backed by legislation to ensure it was doing its job properly.
Party leaders said the new independent regulator - with powers to demand up-front apologies from UK publishers and impose £1m fines - would protect victims of press intrusion and preserve press freedom.
A new piece of legislation means the charter outlining the regulator's powers can only be changed with a two-thirds majority in both houses of Parliament.
And a second new piece of law also means judges could award punitive damages against publications which refuse to sign up to a new watchdog, in the event of a court case if a complaint could have been resolved through arbitration.
The Times said in its editorial that Monday had been "a bleak episode in the story of freedom of the press in Britain" and that "the principle that a free press not subject to Parliamentary statute has been conceded".
The extent to which the new regulation applies to the internet is not yet clear.
On Monday, Culture Secretary Maria Miller said that to be affected by the change, a "publisher would have to meet the three tests of whether the publication is publishing news-related material in the course of a business, whether their material is written by a range of authors - this would exclude a one-man band or a single blogger - and whether that material is subject to editorial control".
She said the new rules were designed to protect "small-scale bloggers" and to "ensure that the publishers of special interest, hobby and trade titles such as the Angling Times and the wine magazine Decanter are not caught in the regime".
Guidance issued by the Department for Culture, Media and Sport (DCMS) suggests "online-only edited 'press-like' content providers" - such as the Huffington Post and Holy Moly Gossip - would be relevant publishers.
A DCMS spokeswoman said: "Ultimately, it is a matter for the court to decide on the definition of a relevant publisher based on assessment of the facts, in accordance with the three interlocking tests - course of business, range of authors and editorial control."
The charter defines news publishers as newspapers, magazines or websites containing news-related material.
However, the government had conceded there was some confusion about how the charter applies to some news-based websites.
Carla Buzasi, editor-in-chief of the Huffington Post UK, told BBC Radio 4's Today programme she was "concerned" that there was confusion over who was covered, adding that she felt the agreement had been "rushed".
Harry Cole, who writes for the Guido Fawkes political blog, said the regulatory changes had been implemented in a "chaotic fashion".
"They don't understand that [the internet] is the future. There are not necessarily going to be newspapers in 10 years," he said.
"The news brands will survive, but we are all bloggers now - things are published on the internet, so this needs to be addressed before these things are set up."
Mr Cole added: "On a matter of principle, we would be opposed to a regulator - especially one accountable to the politicians we write about every day."
Local paper concerns
The Newspaper Society, representing local papers, said the proposals agreed by the three parties would place "a crippling burden on the UK's 1,100 local newspapers, inhibiting freedom of speech and the freedom to publish".
That was, in part, because of the "huge financial penalties for newspapers which choose to be outside the system and an arbitration service which would open the floodgates to compensation claimants", president Adrian Jeakings said.
But Chris Blackwood, editor of the Independent, told BBC News: "We don't think it's too bad - it could have been a lot worse."
He added: "I think we have to recognise the mess the industry got into. I mean, the industry did some very bad things and our existing regulator just wasn't up to the task."
The 57-nation Organisation for Security and Co-operation in Europe (OSCE), meanwhile, warned that "a government-established regulatory body, regardless of how independent it is intended to be, could pose a threat to media freedom".
Prime Minister David Cameron said the Conservatives, Liberal Democrats and Labour had agreed on a new system of "tough independent self-regulation that will deliver for victims and meet the principles set out in [Leveson's] report".
He said a new system would ensure:
- upfront apologies from the press to victims
- fines of 1% of turnover for publishers, up to £1m
- a self-regulatory body with independent appointments and funding
- a robust standards code
- a free arbitration service for victims
- a speedy complaints system