He served as Minister of Science, Education and Sports in the 9th and 10th government of Croatia under HDZ's Ivo Sanader, and was a presidential candidate in the 2009 and 2024 elections.
He defended his doctoral dissertation, entitled "Osteogenesis Imperfecta as a Result of Faulty Processing of Messenger RNA", in 1997 at the University of Zagreb, Medical School (results were obtained at the University of Connecticut Medical School in Farmington, CT, USA).
He was also trained at the Connecticut State Police Forensic Science Laboratory, Meriden, the Armed Forces Institute of Pathology (AFIP), Rockville, the Analytical Genetic Testing Center, Inc., Denver, the university hospital St. Christopher's, Allegheny University, Philadelphia, and the Roche Molecular Systems, Alameda, all in the United States.
Primorac became a politician as a member of the Croatian Government, serving as the Minister of Science, Education and Sports between 2003 and 2009.
Primorac proposed the National Programme of Measures for the Implementation of Compulsory Secondary Education to Croatian Parliament, based on Article 80 Constitution of the Republic of Croatia.
During its session on June 21, 2007, Parliament adopted the program as the optimal model to solve the problems of poor education structure of Croatian population, and the frequency of early school dropouts.
The programme Unity through Knowledge yielded approximately 40 competitive research projects with returnee and Diaspora (Croatian professionals working abroad) participation.
On June 16, 2009, weekly magazine Nacional announced that "Primorac will soon become the first minister in the history of Croatia to resign at the peak of his political career".
In the newly formed government of Jadranka Kosor, he was replaced by his former state-secretary Radovan Fuchs, who reversed Primorac's free schoolbook policy in his first week in office.
[19] In the first round of the election on 29 December, Primorac placed second with 19% of the vote, but was able to compete in a runoff scheduled in January 2025 after Zoran Milanović narrowly failed to win an outright majority.
In 2016 he was appointed as a visiting professor at the College of Medicine and Forensics, Xi’an Jiaotong University, People’s Republic of China.
For two years (2000–2002) he was the main coordinator of an international project supported by Promega, which brought together six European countries with the aim of applying and analyzing new DNA methods for the purpose of identification.
Primorac is the founder of the American-European School for Clinical and Forensic Genetics which is being held bi-annually in Croatia and co-founder of the International Society of Applied Biological Sciences.
Several renowned media outlets, both electronic and print, have reported on the results of his research work, such as the New York Times,[22] USA Today, Chicago Tribune,[23] Hartford Courant, JAMA, Lancet, Science, NBC, Channel 8 (Connecticut TV Station), etc.
He was also director of the Polyclinic " Holy Spirit II " in Zagreb while currently, he is President of the Board of Trustees of the St. Catherine Hospital.
[24] That laboratory was the first in the region where identification of war victims discovered in mass graves by DNA technology took place.
Primorac played a role in the founding process of the initially private Media university in Split, that subsequently relocated to the inland city of Koprivnica.