The government said NHS boards were almost fully compliant
Concerns have been raised that not all of the NHS in Scotland is ready to cope with new limits on working hours.
The European Working Time Directive means doctors are now not supposed to work more than 48 hours a week.
BMA Scotland has warned that there could be a significant proportion of junior doctors working in non-compliant posts as the legislation comes in.
The Scottish Government said it expected NHS boards to be 96% compliant with the regulations.
The BMA said that data from the end of May showed 38% of junior doctor posts were still not compliant with the 48 hour working week.
It has warned that the implementation of a 48 hour week will see a "massive rise" in the number of junior doctors working in non-compliant posts.
The organisation has also said there was the possibility of disruption to patient services in August and that the quality of training for junior doctors could be threatened.
Dr Alan Robertson, chairman of BMA Scotland's junior doctors committee, said the organisation was broadly in favour of the legislation in terms of a striking a good work-life balance.
But he said there were fears some junior doctors could be pressured to lie about their hours.
He told BBC Scotland: "At present many of the rotas that juniors work on are technically 48-hour compliant on paper, it's the reality of that that we need to look at.
"A lot of rotas certainly in the past year have had gaps on them, which have made it difficult to be fully compliant, and there is also concern about the pressure on trainees at times to under-report their hours on their monitoring forms."
Mr Robertson said some juniors in the surgical specialties also felt concerned that the reduction in hours could mean them missing out on previous levels of training in the practical skills.
The working hours of doctors in training should average 48 hours a week or less over a 26 week reference period starting from 1 August.
A Scottish Government spokeswoman said: "The Scottish Government is closely monitoring NHS Boards' actions towards achieving compliance with the EWTD and we are providing support via the Working Time Regulations Advisor to ensure they achieve compliance.
"The advisor is visiting boards to support them in rota and service redesign, while boards continue to invest in new roles for medical and non-medical staff and to expand the Hospital at Night model which will reduce junior doctors' hours."