The polling was conducted from 13th to 20th December, among a representative sample of 1,012 people in Scotland, and 1,011 people in the rest of the UK. Panelbase is a member of the British Polling Council.
The details are:
"Do you think that there should be a televised referendum debate between Scottish First Minister Alex Salmond to argue the case for an independent Scotland, and UK Prime Minister David Cameron to argue the case for the UK?"
FINDINGS AMONG PEOPLE IN SCOTLAND
Don't Know: 11%
Among people who voted Labour in the Scottish Parliament constituency vote in 2011, 57% want a Salmond/Cameron debate with 27% against; 50% of Lib Dem voters want such a debate with 38% against; 79% of SNP voters want a debate with 15% against; and 35% of Tory voters back a debate with 54% against.
FINDINGS AMONG PEOPLE IN REST OF UK
Don't Know: 19%
Among people in the rest of the UK who voted Tory in the 2010 Westminster General Election, 57% want a Salmond/Cameron debate with 34% against; 65% of Labour voters want such a debate with 18% against; and 65% of Lib Dem voters back a debate with 22% against.
Welcoming the figures, the Deputy First Minister and SNP Depute Leader Nicola Sturgeon said:
"These figures demonstrate that there are decisive majorities in Scotland, and among people in the rest of the UK, for a televised referendum debate between Alex Salmond and David Cameron. In Scotland, most Labour, SNP and Lib Dem voters want a debate between the First Minster and Prime Minister; and in the rest of the UK they are joined by a clear majority of David Cameron's own Tory voters, as well as Labour and Lib Dem supporters.
"Yet while David Cameron is happy to pull the strings of the No campaign from 10 Downing Street, he is scared to debate Alex Salmond face-to-face. As the leading politician seeking a No vote, Mr Cameron has to find his courage in referendum year.
"David Cameron's government has boasted that 'Whitehall's full intellectual might' is engaged in trying to achieve a No vote in the referendum, with the Treasury spearheading a 'co-ordinated push' - resulting in 13 reports being produced across UK government departments to support the No campaign.
"It is abundantly clear that the No campaign is Tory-led and Westminster-led - a fact further underlined by the Prime Minister's New Year message.
"Therefore, as the principal signatories of the Edinburgh Agreement, the natural progression in these circumstances is a televised, head-to-head debate between Mr Cameron and Alex Salmond - a democratic position supported by a substantial majority of people north and south of the border.
"It is not possible, with any degree of consistency or credibility, for the Prime Minister to involve himself and his government so centrally in the referendum process, and then refuse to publicly debate these very issues.
"David Cameron's government has changed its mind on many matters since coming to office - this New Year is the time for him to change his mind on facing Alex Salmond in a TV debate."