Public spending watchdog Audit Scotland found only three health boards had met the Scottish Government's legally binding "treatment time guarantee" since it was introduced in October last year.
The guarantee - included in the SNP's flagship Patients Rights Act - was designed to ensure that inpatients and day case patients were treated within 12 weeks of their treatment being agreed.
However, only NHS Orkney, NHS Western Isles and the Golden Jubilee National Hospital at Clydebank have met their legal duty consistently.
In September, the most recent month surveyed, only six out of 15 health boards achieved the guarantee.
In a further blow to the Scottish Government, a second target to ensure patients wait no more than 12 weeks for their first outpatient appointment is also being missed increasingly by hospitals, the report found. A total of 11,544 people were waiting more than 12 weeks for an outpatient appointment in September, nearly double the number recorded at the same point in 2012.
The Audit Scotland report, out today, said health boards had found the 12-week inpatient guarantee "challenging".
It added: "NHS boards failing to meet the waiting times standards indicates pressure on their capacity.
"There are risks this pressure will increase as demand continues to grow."
The figures sent a serious warning to the Government, nurses' leaders said, while Scottish Labour described them as a shambles.
The findings emerged as health boards' performances were reviewed following a scandal over patients' waiting times being manipulated by NHS Lothian. Patients in that area were marked "socially unavailable" for treatment if they refused to travel to hospitals in England at short notice.
Today's report said the Scottish Government and NHS had taken steps to improve the management and monitoring of waiting lists.
But watchdogs said due to IT changes and the new 12-week guarantee, health boards were now publishing less information about their waiting times.
Royal College of Nursing Scotland Director Theresa Fyffe said: "This update is another serious warning shot across Government's bows to look again at the capacity within health boards to meet their waiting times targets."
Calling for a review of staffing and resources, she added: "All those working in our NHS know that behind all these statistics and figures are people - patients waiting to be treated in a system that's creaking under the strain."
Dr Brian Keighley, chairman of the BMA in Scotland, said: "Quality patient care and clinical priorities must remain the priority and should not be compromised by the legal requirement to achieve targets, particularly at a time when there are rising pressures on NHS capacity, falling budgets and increasing consultant vacancies."
Health Secretary Alex Neil said: "This report shows just how much progress has been made in improving the management of waiting lists across Scotland.
"In addition, we are continuing to support health boards to ensure they deliver waiting time standards and the waiting times guarantee. Health boards across Scotland are investing over £67 million this year in creating additional capacity to be able to treat more patients than ever."
Patients not treated in the timescale are entitled to an explanation from the health board and to have other arrangements put in place to ensure their treatment starts as soon as possible.