BBC director general Lord Hall has written to the Democratic Unionist Party (DUP) to explain why they are not being invited to participate in televised leaders' debates.

The DUP has protested at a format for the proposed debates set out by the four major broadcasters, which includes leaders from Ukip, the Greens, the Scottish National Party and Plaid Cymru alongside the big three parties, but no representatives of Northern Irish parties.

Prime Minister David Cameron has said that he wants Northern Irish parties included, leading to accusations from Labour that he is seeking to duck the debates.

Lord Hall responded to a letter from the DUP - which has eight MPs at Westminster to the SNP's six, Plaid's three, Ukip's two and the Greens' one - to say that the position set out by the broadcasters had not changed.

Because the party political structure in Northern Ireland is different from that of the rest of the UK, the position of the DUP was not directly comparable with that of the SNP and Plaid, which will be competing with Conservative, Labour and Liberal Democrat candidates in constituencies where they stand.

If the DUP was invited to take part, impartiality rules would require all of the Northern Ireland parties to be given a spot, the director general wrote.

DUP leader and Northern Ireland First Minister Peter Robinson described the BBC response as "irrational".

In a message on Twitter, Mr Robinson said he had "received irrational response from BBC DG re: debates. No valid reason for DUP's exclusion offered."

He said Lord Hall had "offered excuse that they couldn't invite one NI party without the others", adding: "Ignores fact that three parties currently invited stand in NI."

The broadcasters are proposing a revised 7-7-2 format, under which two debates hosted by BBC and ITV would feature the leaders of the Conservatives, Labour, the LibDems , Ukip, the Greens, the SNP and Plaid Cymru, and a third on Channel 4 and Sky would pit Mr Cameron against Ed Miliband.