Yesterday the BBC revealed it had reached the deal with newspaper groups Daily Mail & General Trust, Guardian News and Media, Telegraph Media Group and Independent News & Media.
Trinity Mirror and News International, the other major newspaper groups, have no plans to take up the BBC's offer to host its video news on their websites.
News International's criticism was reported last night by The Guardian, which quoted an explanation from a company spokeswoman as to why the owner of The Times and The Sun was unhappy with the terms stipulated by the BBC
She said: "News International assessed the BBC's proposals and found that they not only impose onerous marketing conditions, but also offer little differentiation or benefit to customers of our websites.
"We expect the BBC will require the Daily Mail, Guardian, Daily Telegraph and Independent to provide marketing for the BBC at no cost, including embedding a BBC player (rather than using their own), featuring BBC pre-roll "stings" on the content, linking to the BBC and accepting a ban on advertising.
"This means that while they may not be charged, it is certainly not free and is likely to bring about a greater sameness of video content on a range of sites."
The BBC issued the following statement in response to the comments: "The primary goal with all the BBC's partnership proposals is to explore partnerships which support public service broadcasting and wider access to PSB content for audiences.
"The aim of this particular partnership is to open-up access to BBC news content and allow other newspapers to use it to complement news content on their websites.
"The content has already been published on BBC Online and it's only right it's marked as coming from the BBC - audiences would expect us to acknowledge that. It's entirely up to newspapers whether they want to choose to embed the content or not - some have taken a different view to others."
The corporation is also under fire from commercial news supplier ITN, which said yesterday its offer distorts the market and undermines investment by commercial companies.