The 111 service, replacing NHS Direct, is due to launch in England on Monday.
The British Medical Association's letter to Sir David Nicholson follows reported problems in trial areas.
Health Minister Lord Howe has said some areas will have more time to go live with 111 while "thorough testing" to ensure reliability is carried out.
Lord Howe has already admitted the new 111 telephone advice service - which the government has said will ease pressure on emergency 999 phone lines - had run into "teething problems".
But the BMA said that in several areas it seemed to have been completely unable to cope with call volumes or suffered severe IT failures.
It said patient safety was being put at risk.
Dr Laurence Buckman, chairman of the the BMA's GP committee, said: "There have been widespread reports of patients being unable to get through to an operator or waiting hours before getting a call back with the health information they have requested,
"In some areas, such as Greater Manchester, NHS 111 effectively crashed because it was unable to cope with the number of calls it was receiving. The quality of advice being given out has also been questionable in some instances."
He said the "chaotic mess" of 111 was "placing strain" on overstretched parts of the NHS, such as the ambulance service, and potentially placing patients at risk.
"The BMA has been warning the government about the problems with NHS 111 for almost two years. They must finally act to ensure that patient safety is guaranteed," he added.
The BMA said it had written to NHS chief executive Sir David Nicholson to call for a delay to the launch of 111 until it was "fully safe for the public".
Dr Buckman said: "We cannot sacrifice patient safety in order to meet a political deadline for the launch of a service that doesn't work properly."
The Department of Health has already sanctioned an extension of up to six months of the original 1 April 2013 deadline for regions struggling to set up the new service.
The NHS Direct 0845 4647 service will continue to be available to callers in areas where the NHS 111 service is not yet available, Lord Howe has said.
These include: North of Tyne and Tees, North Essex, Bedfordshire and Luton, Cambridgeshire and Peterborough, Leicestershire and Rutland, Berkshire, Cornwall and Devon.
The organisation representing British doctors has written to NHS bosses to call for a delay in the launch of a new non-emergency telephone advice line.