Czech term (edited): magistersk� studijn� program

"he earned his medical degree" is the wording I've seen when looking at physicians' bios
He earned his medical degree in a graduate-level program in general medicine.
Considering the differences between the Czech and US educational systems, I find this to be the safest way to put this phrase.

"program leading towards the degree of Doctor of Medicine"
He has received his university education in the program leading towards the degree of Doctor of Medicine.
I've inadvertently hidden this answer and I can't get it to appear again. So, this is my original suggestion and read Zenny's answer with this in mind.
As regards the degrees in medicine, the best overview of degrees granted in the USA can be found at:
www.ama-assn.org/ama/pub/category/2320.html

The education of physicians in the United States is lengthy and involves undergraduate education, medical school, and graduate medical education (the term graduate medical education [GME] includes residency and fellowship training; the American Medical Association does not use the term "postgraduate education"):
- Undergraduate Education--4 years at a college or university to earn a BS or BA degree, usually with a strong emphasis on basic sciences, such as biology, chemistry, and physics (some students may enter medical school with other areas of emphasis).
- Medical School (undergraduate medical education) -- 4 years at one of the LCME-accredited US medical schools, consisting of preclinical and clinical parts. After completing medical school, students earn their doctor of medicine degrees (MDs), although they must complete additional training before practicing on their own as a physician.
- Residency Program (graduate medical education) -- Through a national matching program, newly graduated MDs enter into a residency program that is 3 to 7 years or more of professional training under the supervision of senior physician educators. The length of residency training varies depending on the specialty chosen: family practice, internal medicine, and pediatrics, for example, require 3 years of training; general surgery requires 5 years. (Some refer to the first year of residency as an "internship"; the AMA no longer uses this term.)






--------------------------------------------------
Note added at 19 hrs 26 mins (2004-05-05 15:12:54 GMT)
--------------------------------------------------

\"Graduate-level program\" in my suggestion corresponds to \"magisterské štúdium\", which is how physicians get their degree in Slovakia and the Czech Republic.
We need to be very careful to avoid any connection with \"graduate MEDICAL education\" that is the next step in the educational process for doctors.