Under plans to speed up fitness-to-practise cases, doctors would be able to avoid public hearings if they accept sanctions proposed by the GMC.
Overall, 83% of respondents agreed the GMC should explore alternatives to public hearings in cases where there is no significant dispute about the facts.
A further 77% said it would be appropriate for the GMC to have discussions with doctors to encourage them to accept a sanction.
Some felt that this would mean doctors could avoid lengthy suspensions while they wait for a hearing. But a 'small minority' of respondents felt doctors would feel pressured into accepting sanctions. Concerns were raised that it would lead to a loss of transparency and the perception of 'deals being done behind closed doors'.
The GMC said information about cases which are resolved without a hearing would be available to the public, after more than half of respondents said this would help maintain confidence in the profession.
GMC chief executive Niall Dickson said the GMC was committed to making the processes open and transparent.
'Information about cases resolved without a hearing will be available to complainants and the public,' he said.
Meanwhile, the GMC also said there was strong support for plans to automatically erase from the register doctors with serious criminal convictions.
Offences including murder, rape, child abuse, people trafficking and blackmail should trigger immediate erasure, 81% of respondents said.
A total of 72% of respondents also agreed that doctors should be suspended if they fail to co-operate with GMC investigations and repeated attempts of engagement.
Mr Dickson said: 'We will work closely with doctors and patients to make sure the changes ensure there is widespread confidence in our procedures.'