Of 6,674 RCGP members who took part in a survey commissioned by the college, 47% agreed the college should remain opposed to a change in the law on assisted dying.
A total of 40% backed altering the college's stance towards supporting a change in the law 'providing there is a regulatory framework and appropriate safeguarding processes in place', while 11% of respondents backed a neutral stance and 2% abstained.
The results show a significant shift in views among RCGP members since the college last polled doctors on assisted dying - with a 2013 poll finding that 77% of members at the time felt the college should oppose changing in the law on assisted dying.
The results come less than a month after the BMA announced plans to ballot members on its stance on assisted dying for the first time.
Under current laws assisted dying is illegal throughout the UK. After agreeing that the latest poll findings do not support a change in the college's stance, the RCGP has agreed that unless there are 'significant developments' it will not consult again for at least five years.
RCGP chair Professor Martin Marshall said: 'As the UK’s largest medical royal college it is important that we engage in debate and listen to what our members have to say on wide-ranging issues affecting GPs and their patients.
'Assisted dying is a controversial topic and this was reflected in the responses to our consultation. However, the highest proportion of respondents said that the college should continue to oppose a change in the law on assisted dying.
'This was the largest consultation on an issue of public policy that the college has conducted both in terms of response rate and volume of respondents. The role of the college now is to ensure that patients receive the best possible palliative and end of life care, and to this end we are working with Marie Curie and others to support this.'
However, the charity Dignity in Dying said it could see no reason why the college had not decided to move to a neutral stance on assisted dying given that there was no longer a majority among its members opposed to changing the law.
The charity's chief executive Sarah Wootton said the latest poll showed an 'emphatic shift' in the views of doctors since 2013 - and pointed out that the 'vast majority' of the general public want to see assisted dying laws change.
Polling by Dignity in Dying in 2015 found 82% of respondents supported legalising assisted dying for people who are terminally ill, and polling for another charity last year found even higher support.
Ms Wootton said: 'Parliament should take note of this dramatic shift in medical opinion: the proportion who feel the RCGP should oppose a change in the law has plummeted from 77% to less than half, and those who want the college to support change has increased eight-fold to 40%.
'The Royal College of Physicians’ (RCP) survey last year also demonstrated that there is now a wide spectrum of views in the medical profession towards supporting greater patient choice at the end of life, and the policies of medical organisations need to reflect that.
'The RCP sensibly and pragmatically took the decision to drop their longstanding opposition in favour of neutrality, and there is no reason why the RCGP should not follow suit.'