Almost two-thirds of voters think Culture Secretary Jeremy Hunt should resign, according to a poll published by ComRes for The Independent.
It comes as pressure mounts on the minister over his dealings with the Murdoch empire during News Corporation's bid to buy all of broadcaster BSkyB.
The ComRes poll results found:
- 63% feel that he should quit
- 12% thought he should remain in his post
- 24% said they did not know
- Even among Conservative supporters, 49% to 27% think Mr Hunt should resign
- On voting intentions, Labour is five points ahead on 39%
- Conservatives are unchanged on 34% and the Liberal Democrats down one on 10%
Earlier, Lord Justice Leveson turned down a request from Hunt to bring forward his evidence at the inquiry into media ethics "in the interests of fairness to all".
Mr Hunt had requested an earlier appearance so that he could answer allegations about his handling of News Corporation's BSkyB takeover bid.
A date has still not been set, but politicians will not be called until mid-May, meaning the Culture Secretary will have to wait at least a fortnight and possibly much longer.
According to a report in today's Telegraph, Leveson will also not rule on whether Hunt broke the Ministerial Code in his dealings with the Murdochs.
David Cameron is prepared to consider ordering an investigation into Hunt's dealings with News Corporation but not until he has appeared at the Leveson Inquiry.
Deputy chairman of the Conservative Party Michael Fallon said a probe was possible.
Labour leader Ed Miliband said the Prime Minister should have fired Mr Hunt and at the very least should refer the matter urgently to independent adviser on ministerial interests, Sir Alex Allan.