Czechs have always been conscious of their rich musical tradition, and although Jiří Bělohlávek, who has died aged 71, started out as a student of the cello, he became the greatest conductor of the Czech repertoire after Václav Talich and Václav Neumann, passing on this legacy to outstanding former students Jakub Hrůša and Tomáš Netopil.

Bělohlávek will be best remembered for his luminous interpretations of Janáček and Martinů, whose claim as the last towering voice of the 20th century, although insufficiently recognised as such outside the Czech republic, he has done more than anyone to further. He also proposed as a native Czech Gustav Mahler, who was born in Kaliště, in the Bohemian region of what was then the Austrian empire. His Mahler cycle with the BBC Symphony Orchestra, of which he was ultimately chief conductor (2006-12), with majestic performances of the Ninth Symphony in 2003 and the Third in 2007, set him alongside the greats.

Prague, where he was born to Jiří Bělohlávek, a judge, and his wife, Anna, nurtured his musical education. Having studied as a cellist with Miloš Sádlo, he graduated from the Prague Conservatory and Academy of Performing Arts. His first major steps as a conductor were taken under the guidance of the magnetic and idiosyncratic Romanian Sergiu Celibidache. While he never applied the master’s later approach of slow tempi for just about everything, he did reflect his unhurried study and concern for textural detail.

Bělohlávek won the Czech national conducting competition in 1970, and subsequently worked with the Brno Philharmonic, essentially Janáček’s orchestra from the capital of the composer’s beloved native Moravia. He became known to British audiences when he appeared at the Edinburgh festival in 1990 with the Prague Symphony Orchestra, of which he had been principal conductor from 1977 to 1989.

Parallel with Charles Mackerras’s pioneering work on Czech music, Bělohlávek started to set the seal on the true worth of Martinů – the fourth great Czech composer, chronologically, after Smetana, Dvořák and Janáček – with a searing Usher Hall concert performance of Martinů’s last full-length opera, The Greek Passion, and, another revelation, of the second of the four piano concertos, with a Czech soloist who had known the composer well, Rudolf Firkušný.

That September, Bělohlávek became chief conductor of the Czech Philharmonic Orchestra, but this first tenure was short-lived; following a dramatic reorganisation of the orchestra, he resigned in 1992. His big project then was the founding of the Prague Philharmonia the following year, first with government funding and then with the help of private sponsorship, to train 40 young musicians. They appeared together at the BBC Proms in 2004.

Meanwhile, his work with the BBC Symphony Orchestra took him from principal guest conductor (1995-2000) to chief conductor, and he was then named conductor laureate in 2012. On succeeding him as the orchestra’s chief conductor in 2013, Sakari Oramo was “pretty impressed actually with the sound and attitude already then, and I think much of it actually owes to Bělohlávek and his work. His aesthetic background is, I feel, somehow similar to mine. He’s a string player, a cellist [Oramo is a violinist], and he’s got this middle European sound ideal, which I still find works in the orchestra and I’m happy to build on it. I think it’s the first time I’ve come to an orchestra with a sorted string section.” The handsome sound he fostered was especially apparent in the highest achievement of his tenure, alongside the season-by-season work on a Mahler cycle – his single-season introduction, to British audiences who would have been largely unfamiliar with most of them, to the six Martinů symphonies. To hear the moving, elevated finale of the Third was rather like being present at the premiere of a masterpiece. Even Martinů enthusiasts would have had very few chances to hear this work live in the UK.

The programmes, usually featuring three other works contemporary with the half-hour symphonies, were exhausting for the players, but the results were extraordinary and have been preserved on CD. Bělohlávek has a large Martinů discography with a number of orchestras. The annual opera in concert with the BBC Symphony was also a great event, above all the revelations of Martinů’s Juliette and Smetana’s Dalibor, and there was superb work at Glyndebourne in 2003 on Wagner’s Tristan und Isolde and in 2009 on Dvořák’s Rusalka. He made his debut at the Metropolitan Opera New York with Janáček’s Kát’a Kabanová in 2004.

In 2007 he was the first non-native English speaker to conduct and make the traditional speech at the Last Night of the Proms at the Royal Albert Hall. At the Last Night in 2009 he operated a vacuum cleaner in Malcolm Arnold’s A Grand, Grand Overture. His trademark mop of grey hair was often seen in the arena; he loved promming.

Last year he conducted the Czech Philharmonic and an outstanding cast in Janáček’s Jenůfa at the Royal Festival Hall, and returned to the Proms for the same composer’s The Makropoulos Case, with the Finnish soprano Karita Mattila outstanding as the 337-year-old heroine and the BBC Symphony Orchestra glowing. The opera’s shattering acceptance of the human condition, with the protagonist telling onlookers in the great final scene “you are so blissful, for the trivial chance reason that you are going to die so soon”, had a special resonance, since he was then being treated for cancer. At his last London appearance in April, for Dvořák’s Requiem, and last ever concert, in May, with the Prague Philharmonia playing Martinů, he was, as ever, promoting Czech masterpieces to the wider world.

He is survived by his wife, Anna Fejérová, whom he married in 1971, and their daughters, Susanna and Marie.

• Jiří Bělohlávek, conductor, born 24 February 1946; died 31 May 2017