Rishi Sunak has said he hopes the BBC can resolve its row with Gary Lineker in a “timely manner” but the dispute is not something the government should get involved in.
In a statement, the prime minister said Lineker “was a great footballer and is a talented presenter”.
But the 62-year-old Match of the Day host’s dispute with the BBC over his use of social media is “rightly a matter for them, not the government”, he added.
The BBC has acknowledged the “strength of feeling” among staff as programmes including Football Focus and Final Score were taken off air.
Presenters, pundits and commentators refused to appear.
It is understood that Saturday’s edition of Match of the Day will be limited to 20 minutes.
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The row began after Lineker made critical remarks about the government’s Illegal Migration Bill.
In his statement, the prime minister defended the new policy on stopping migrants crossing the Channel, adding that given the “seriousness of the issue at hand” it was important to “maintain perspective”.
He said: “Forty-five thousand people crossed the channel illegally in the 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.”
The row began on Tuesday when Lineker tweeted comments comparing the language used by the government to that used in 1930s Germany, when the Nazis came to power.
The BBC deemed the tweet had broken its editorial guidelines on impartiality and said Lineker had been removed from Match of the Day until an agreement could be reached on his use of social media.
Lineker did not answer reporters’ questions when he left his home in southwest London, on Saturday morning.
The 62-year-old former England striker then travelled to Leicester’s King Power stadium to see his hometown club play Chelsea in the Premier League.