In his soloist and pedagogical career Končar was particularly dedicated to the interpretation of works of Johann Sebastian Bach (solo sonatas and partitas), also to the repertoire on which he worked with Max Rostal (W.A. Mozart and the French repertoire – M. Debussy and C. Franck), with Yfrah Neaman (J. S. Bach, M. Bruch, E. Bloch, F. Mendelssohn) and Leonid Kogan (Russian literature – P.I. Tchaikovsky, A. Glazunov, A Khachaturian, S. Prokofiev and D. Shostakovich – for the performance of which he won a Russian award as the first foreigner ever to receive it).
He continued dedicating special attention to the performance of 20th century classics (B. Bartok, B. Martinu, S. Gubaidulina, A. Nilsson, K. Goldmark) as well as contemporary works, on account of which a range of composers dedicated their compositions to him (Boris Papandopulo, Milko Kelemen, Giuseppe Gavazza, D. Holloway and Ivo Malec).
Since 1988 Končar has been teaching at the Zagreb Music Academy. He held master classes in Madrid, Berlin, Turin, Milan, Sidney, Tokyo, Matsumoto, Beijing, Stellenbosch and elsewhere. In the year 2004 he initiated the LAUS Summer Academy in Dubrovnik, together with some of the greatest world violinists (Zakhar Bron, Viktor Tretyakov, Dmitry Sitkovetsky, Leonid Sorokow) and 2010 established first ever Music Academy in Mostar (Bosnia and Herzegovina).