Cabinet minister Michelle Donelan has paid an undisclosed sum and apologised to a professor after falsely suggesting she supported Hamas.
The science secretary made the claim about Prof Kate Sang, an academic at Heriot Watt University, in a letter posted on social media in October.
The sum paid was covered by taxpayers to prevent prolonged legal costs, the BBC has been told.
Prof Sang said Ms Donelan had attacked her to make a “cheap political point”.
The letter followed the appointment of Prof Sang, as well as Dr Kamna Patel of University College London, to an advisory group on equality, diversity and inclusion at UK Research and Innovation (UKRI), a public body which manages the government’s research funding.
Ms Donelan accused both women of sharing extremist content online and claimed they had breached the Nolan principles, which set out how public officials should behave.
She also suggested Professor Sang had expressed sympathy and support for Hamas.
Prof Sang had earlier shared a Guardian article about government plans to clamp down on pro-Palestine marches and called the plans “disturbing”, while Dr Patel had retweeted a post describing Israel’s actions in Gaza as “genocide and apartheid”.
Ms Donelan – who has been secretary of state for science, innovation and technology since July – spoke of her “disgust and outrage” at the appointments and called on UKRI to remove both women from the group.
A months-long investigation by UKRI found no evidence that either Prof Sang or Dr Patel had breached their roles’ terms of reference or the Nolan principles.
In a statement posted to X on Tuesday, Ms Donelan admitted she was wrong and had “misunderstood” the social media posts.
She said she had deleted her original post and fully accepted that Prof Sang was “not an extremist, a supporter of Hamas or other proscribed organisation”.
Hamas, or in some cases its armed wing alone, is considered a terrorist group by Israel, the US, the EU, and the UK, among others.
Prof Sang said: “I am delighted that this matter has now concluded, but very disturbed by the way in which Michelle Donelan and UKRI behaved.
“Had they asked me at the start, I would have explained the true position. Instead, Michelle Donelan made a cheap political point at my expense and caused serious damage to my reputation.
“I propose to donate part of the damages she has paid to a charity.”
Dr Patel described the experience as “distressing”, saying she was “glad” the process had concluded.
She said: “There was never any need for UKRI to investigate as it should have been obvious from the start that we had not breached the Nolan principles or expressed extremist views.”
A Downing Street source said Prime Minister Rishi Sunak had “full confidence” in “excellent minister” Ms Donelan.
Shadow science secretary Peter Kyle said accusing a researcher of sharing extremist material and sympathising with a proscribed group was a “new low in government standards”.
The payment to Prof Sang came from the Department for Science, Innovation and Technology (DSIT).
The payment was made to reduce the overall costs to the taxpayer that could result from protracted legal action, the BBC understands.
Lib Dem deputy leader Daisy Cooper said the public would be “shocked” by the use of taxpayer funds for the payment and called for a Cabinet Office inquiry to establish “exactly what happened, whether any rules were broken and how much public money was spent”.