In 2012, the stillbirth rate fell to 4.7 per 1,000 births, the lowest in the UK, while infant deaths fell to 3.7 per 1,000, the Scottish Government said.
The rate of perinatal deaths, which refers to stillbirths and deaths in the first week of life, was 6.5 per 1,000.
Stillbirth rates were as high as about 12 per 1,000 in 1974.
Maternal obesity, smoking, alcohol consumption, advanced maternal age, substance misuse and lack of maternal employment were all associated with an increased probability of fetal and infant deaths, according to the Government.
Public health minister Michael Matheson said: "Ultimately, the most important thing a mother can do to protect her baby is visit her midwife or local maternity services as soon as she finds out she is pregnant. Midwives and healthcare professionals can identify any risks that could affect the health of the baby and tailor advice and support that is appropriate to both the mother, and their partner.
"The Scottish Government introduced strict targets in 2012 for health boards that aim to increase the number of women accessing high quality antenatal care early on in their pregnancy. We have also invested in maternity champions across health boards and have been carrying out of a lot of work to raise awareness of the issues surrounding stillbirths among healthcare professionals.
"This has included convening a national working group, holding a Stillbirth Seminar in Scotland with the stillbirth charity Sands, and supporting further research into this subject.
"The NHS in Scotland already has some of the safest hospitals in the world, and our patient safety programme is world-leading. This, along with the work we are doing to improve knowledge of stillbirth causes and access to antenatal care, will be instrumental in further reducing stillbirth and infant deaths going forward."
There were 656 deaths notified with the Scottish Stillbirth and Infant Death Survey.