The Prime Minister said the BBC's decision to take Gary Lineker off air is a "matter for them" and "not everyone will always agree" with his asylum policy.
The 62-year-old presenter has been embroiled in a row over impartiality after comparing the language used to launch a new Government asylum policy with 1930s Germany on Twitter.
It prompted criticism from Downing Street, Culture Secretary Lucy Frazer and Home Secretary Suella Braverman, who accused him of "diminishing the unspeakable tragedy" of the Holocaust.
The main presenter of Match Of The Day claimed the BBC "told him" he had to step back from presenting the show amid criticism of his comments about the Government's new asylum policy.
The cooperation said on Friday that it had "decided" Lineker would take a break from presenting the BBC One football highlights show until an "agreed and clear position" on his use of social media had been reached.
Co-hosts Alan Shearer and Ian Wright announced they would be boycotting the show and several of the show's commentators shared a joint statement online, saying they would also be stepping down from Saturday’s broadcast.
Match Of The Day will now go ahead on Saturday night without a presenter, pundits and several regular commentators.
In a previous statement the BBC said the show would "focus on match action without studio presentation or punditry" saying it understood the position of its presenters.
In a statement, released on Saturday evening, Rishi Sunak said: "As Prime Minister, I have to do what I believe is right, respecting that not everyone will always agree. That is why I have been unequivocal in my approach to stopping the boats.
"Gary Lineker was a great footballer and is a talented presenter. I hope that the current situation between Gary Lineker and the BBC can be resolved in a timely manner, but it is rightly a matter for them, not the Government."
Mr Sunak said that while the process is ongoing, it is important that we maintain perspective, particularly given the seriousness of the issue at hand.
He said: "Forty-five thousand people crossed the channel illegally last year, many of whom have been exploited or trafficked by criminal gangs, putting their lives in danger.
"We need to break this cycle of misery once and for all and the policy we set out this week I believe aims to do just that. It is not only the fair and moral thing to do, it is also the compassionate thing to do.
"There are no easy answers to solving this problem, but I believe leadership is about taking the tough decisions to fix problems. I know not everyone will always agree, but I do believe this is fair and right."
Read more:
- The story of Gary Lineker vs the BBC and Match of the Day in 21 Tweets
Ian Wright to quit Match of the Day permanently if BBC sack Gary Lineker
Major BBC update as several shows and post-match interviews scrapped amid Gary Lineker controversy
Alan Shearer won't appear on Match of the Day following Gary Lineker decision
Ian Wright says he won't be doing Match of the Day tomorrow in 'solidarity' with Gary Lineker
