Nigel Farage turned down an interview request by BBC One's Kuenssberg on Sunday due to what he described as a "biased" approach towards him.
Last month the Reform UK leader returned to frontline politics ahead of this week's general election, and according to the polls, his party are neck-and-neck with the Conservatives in second place behind Labour.
On Friday night Farage appeared on Question Time to answer questions from a gathered studio audience, but was left unimpressed after learning that his questioners included a producer for some past BBC shows and a known pro-Palestine activist.
He wrote on X: "I have just been invited to appear on Laura Kuenssberg. I'm refusing until the BBC apologises for their dishonest Question Time audience.
"Our state broadcaster has behaved like a political actor throughout this election. Reform will be campaigning vigorously to abolish the licence fee."
Responding to the claims, a BBC spokesperson said: "We refute these claims. Last night's Question Time audience was made up of broadly similar levels of representation from Reform UK and the Green party, with the other parties represented too.
"There were also a number of people, with a range of political views, who were still making up their mind."
The latest poll analysis suggests that Farage's party could end up with anywhere between five and 89 seats in the House of Commons after Thursday's election.
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