He suggested Britain would not reach many trade pacts in growth markets if it only dealt with nations that meet the level of standards set out in the European Convention on Human Rights (ECHR).
The Foreign, Commonwealth and Development Office (FCDO) said the leaked audio, published by the HuffPost website, had been “deliberately and selectively clipped to distort” Mr Raab’s comments.
Amnesty International UK said the remarks were “shocking” and fitting of a “depressing pattern on human rights from this Government” and Labour said the leak exposed the “shameful truth”.
The comments emerged as the Government comes under pressure not to strike deals with countries suspected of committing genocide.
And it came as ministers published a major review of post-Brexit foreign policy, which includes plans for a “positive trade and investment relationship” with China
During a question-and-answer session with FCDO staff, Mr Raab said: “I squarely believe we ought to be trading liberally around the world.
“If we restrict it to countries with ECHR-level standards of human rights, we’re not going to do many trade deals with the growth markets of the future.”
But, arguing the remarks had been misrepresented, the FCDO shared more of the Foreign Secretary’s response.
“There will be moments, and I can think of behaviour that would cross the line and render a country beyond the pale,” he was said to add.
“But fundamentally I’m a big believer in engaging to try and exert positive influence even if it’s only a moderating influence, and I hope that calibrated approach gives you a sense that it’s not just words – we back it up with action.”
Senior Conservative MPs are among those who have been pressuring the Government on allegations that China is committing genocide against the Uighur minority in the Xinjiang province and human-rights abuses in Hong Kong.
In a Commons statement, Prime Minister Boris Johnson insisted the UK has led international condemnation of China’s “mass detention” of the Uighurs and its actions in Hong Kong.
“There is no question China will pose a great challenge for an open society such as ours,” Mr Johnson said.
“But we will also work with China where that is consistent with our values and interests, including building a stronger and positive economic relationship and in addressing climate change.”
Responding to the leak, an FCDO spokesman said: “We regret that this audio has been deliberately and selectively clipped to distort the Foreign Secretary’s comments. As he made crystal clear in his full answer, the UK always stands up for and speaks out on human rights.
“In his full answer, in an internal meeting, he highlighted examples where the UK has applied Magnitsky sanctions and raised issues at the UN regardless of trade interests, and that this was a responsible, targeted and carefully calibrated approach to bilateral relations.”
But shadow international trade secretary Emily Thornberry said: “The mask has slipped, and the shameful truth of Tory trade policy is revealed.
“Now in private he says the Government is prepared to sign trade deals with any country, even those violating the laws drawn up by British officials after the horrors of the Second World War.”
Amnesty International UK director Kate Allen said the leaked remarks “will send a chill down the spine of embattled human-rights activists right across the globe”.
“This apparent willingness to sacrifice human rights at the altar of trade is shocking, but sadly unsurprising. It fits a depressing pattern on human rights from this Government,” she added.
“Trade is obviously important to all nations, but the Foreign Secretary shouldn’t be throwing human right defenders to the wolves like this.
“So-called ‘growth markets’ – countries like India, Indonesia or Brazil – are often precisely places where human-rights protections are fragile and under threat.”