Mr Williamson claims to have made a 'genuine mistake' after both sportsmen called out the Education Secretary for confusing them.
"Towards the end of a wide-ranging interview in which I talked about both the laptops and school meals campaigns, I conflated the issues and made a genuine mistake," he said.
"We corrected this with the journalist before publication of the story.
"I have huge respect for both Marcus Rashford and Maro Itoje who run effective and inspiring campaigns."
Three Lions star Rashford took to social media to poke fun at the Cabinet Minister for his mistake, suggesting the accent was the biggest giveaway.
Itoje also wrote on Twitter: "Due to recent speculation I thought it was necessary to confirm that I am not Marcus Rashford… And whilst we are here my name is not Mario either!!
"Just a simple Maro Itoje will do… Much love, Marcu… I mean Maro Itoje."
It comes after Williamson claimed he had met Rashford to discuss a review of free school meals policy, with the 23-year-old strongly criticising the government's handling of the situation in the pandemic.
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