Facebook should consider completely removing news from users’ feeds unless it can find a way to avoid low-quality stories clogging up the site, the chief executive of the New York Times has said.

Mark Thompson said he was “terrified” by Facebook’s attempts to use algorithms to rank the quality of news outlets, warning that “a machine entirely behind closed doors is going to rank the world’s news sources” and that publications would be ranked at the top only for as long as they remained “in the good books of Facebook”.

“All of that sounds like a controlled society,” said Thompson, a former director general of the BBC. “The first thing I think they can do is work with us to help users make decisions about who to trust and who not to trust. I don’t want a special pass saying we’re going to be trusted more than others. I want to win people’s trust by people understanding what we’re trying to do.

“We want to create these environments where people have got a chance to make a critical judgment,” he said of Facebook’s attempt to fight disinformation on its platform. “If it can’t be done with something like the Facebook feed then don’t put news on it. If it’s not possible to do it in a way where it’s going to be contextually understood then just use cat videos. If it’s too hard a puzzle then don’t do it.”

Asked whether Facebook should stop promoting news altogether if it could not find a solution to the many problems facing the site, Thompson replied: “I don’t think that’s a crazy idea.”

Such a scorched earth approach is unusual in a media industry that spent the last five years chasing millions of readers via Facebook, only to watch as the traffic fell away this year when Mark Zuckerberg’s company changed the way its algorithm promotes news on the network.

But Thompson is joining a raft of media executives who are looking at life beyond Facebook in the wake of a series of scandals and questions over the sustainability of online news business models. They are trying to ensure their news outlets survive by building a direct relationship with their readers and then asking those readers to pay for quality journalism.

“I think we have a disagreement about what journalism is,” said the executive, who does not have either a Twitter or Facebook account. “Silicon Valley began with a very simple idea of what news was – they thought it was a series of news events. A ship sinks, a building burns down, there’s an earthquake – and news stories were reporting the facts about these events. You’d have 10 events and lots of different outlets reporting the events and the individual reports were interchangeable.

“It’s a crude and positive view of what news is. News is a sophisticated cultural object, it’s very nuanced. Most news stories relate to long-term stories which roll out over years, such as Brexit, the Trump administration or global warming. The ideal relationship a reader has with a news provider is a long-term relationship where they understand the context; they’ve got used to the different voices; they’ve got their criticisms.”

The 61-year-old took over as chief executive of the New York Times in 2012, shortly after it put the majority of its site behind a paywall – a decision that many pundits felt was doomed to fail. The website allows readers to access five articles a month before they have to subscribe.

Aided by its coverage of Donald Trump and Harvey Weinstein, it now has a total of 4 million paid subscribers, including 400,000 who pay for its crossword and cooking section alone, helping to overcome enormous falls in print revenue.

The UK subscriber base is in the “tens of thousands”, but the paper is looking to expand globally and its UK operation now employs about 50 journalists.

Thompson says the paper’s culture has more in common with the BBC than the rough and tumble world of UK newspapers – pointing out that there is “a lot more fact-checking” than on Fleet Street.

“I started reading the New York Times in the 1980s,” he said. “The Times in those days was a very complete part of people’s lives; it was news and opinion and incredibly agenda-setting. It has something of a Radio 4 quality for its heartland audience. What we’re trying to do is to recreate the indispensability of the Times on a smartphone – that’s no mean task.”

The revamp has involved an investment in podcasts such as the highly successful The Daily and some adjustment to how the paper presents its reporting. Thompson despaired after sitting in one-on-one focus groups where one reader, seemingly unaware of the extent of the paper’s foreign coverage but impressed by its digital rivals, said: “You should do what Vice do and get people to leave New York and cover wars.”

Asked about the future of the newspaper industry, Thompson predicted a bloodbath, with mid-sized newspapers obliterated during the transition to digital. Thompson said he spent more time looking at the business models of Spotify and Netflix than other news outlets. “In the US it may be that only two or three titles survive, other than specialists. The Washington Post, the Wall Street Journal and the New York Times have all got decent chances,” he said.

This meltdown was likely to be replicated in the UK, he said, with only outlets that can convince readers to pay for high-quality journalism able to survive as print newspaper revenue collapses. “I don’t think there’s room for every national newspaper to succeed and arguably they’re not succeeding today. How long people want to throw money at that – who knows?”

Thompson is concerned about changing British attitudes towards the BBC and warns that as regional newspapers collapse, “the case for a universally freely available backstop of quality journalism on TV, radio and the web feels like it’s strengthened.”

Thompson, who said he paid to read the Guardian and also checked the New Statesman, Financial Times and BBC, warned of what has already happened in the US, where swathes of local government actions go unreported and uncriticised. “It’s a precious thing the UK’s got and I sometimes wonder if it knows [that].”

For now he still has to contend with his outlet’s most publicly critical reader – one fond of tweeting about the “failing New York Times” despite coming to lunch at the newspaper and calling it a “jewel for America and the world”.

Judging by the timing of Trump’s tweets and the stories he chooses from the White House bedroom, Thompson believes Trump is a fan of the print edition rather than the website.

Thompson said: “We’ve got a faded photograph of Richard Nixon in our boardroom signed by him. It says: ‘Some people read the Times and like it, some people read the Times and don’t like it, but everyone reads the Times.’ As for Donald, he reads it.”