The Cabinet has agreed that a senior minister should face Nick Griffin, the leader of the British National Party, on BBC1's Question Time.
Jack Straw, the Justice Secretary, and John Denham, the Communities Secretary, have both indicated they are willing to sit alongside Mr Griffin.
The decision was disclosed yesterday by Gordon Brown in an interview with Radio City in Liverpool. He said: "I'm not afraid of debating anybody. We have to expose what they are about."
The Prime Minister said the BNP should be tackled on such issues as its attitude to mixed marriage and citizenship and added: "Once these views are known, then people won't want to vote for them."
The cabinet move reverses Labour's previous refusal to share a platform with the extreme right. It has split senior ministers, with the Home Secretary Alan Johnson and the Welsh Secretary Peter Hain both saying they would not debate with Mr Griffin.
The BBC is to invite the BNP leader, who won a seat in the European Parliament in June, to appear on Question Time for the first time next month.
Both the Conservatives and the Liberal Democrats have said they will debate with Mr Griffin on the basis that his policies have to be challenged.
Labour had previously taken the opposite view – that engaging with the BNP gave legitimacy and respectability to its views on race.
But a majority of ministers believe that leaving an "empty chair" alongside Mr Griffin is no longer an option and would help the BNP present itself as outside the political establishment.