He is still active in the sport of running as a coach. Although he had already taken up running in his youth, his serious career only started in the early 1950s under Mihály Iglói, the legendary coach of Tábori"s club, Honvéd Budapest. Already part of the world-record-breaking 1953 and 1954 4 x 1500 metres relay teams of Hungary and the Honvéd Budapest club respectively, he exploded to international fame in 1955, together with Iglói"s other star pupils, Sándor Iharos and István Rózsavölgyi.
On May 28, 1955, he became only the third man in the world to run a four-minute mile, running 3:59.0 and soundly beating both Chris Chataway and Brian Hewson.
(Foreign more than twenty years, he and Rózsavölgyi would remain the only Hungarians to run a four-minute mile) On September 6, he equalled the 1500 metres world record (set just a month earlier by Iharos) with a time of 3:40.8. The occurred at a psychologically unfortunate time for team Hungary, as the Hungarian Revolution of 1956 had just been bloodily crushed by the Soviet military.
(This was all the worse as Honvéd Budapest was at that time the sports club of the Hungarian army) The effects of this were obvious. Iharos missed out on the Olympics entirely, ostensibly due to a minor ankle injury but quite probably because of the revolution, and Rózsavölgyi shockingly went out in the 1500 m heats.
Tábori did much better by comparison.
Expected to medal, he still finished a very respectable 4th in the 1500 metres and 6th in the 5000 metres. After the Olympics, Tábori and coach Iglói didn"t return to Hungary. Instead, they defected to the United States, eventually settling in Los Angeles, California.
Tábori stayed in world class shape for many years, and would have been a medal contender in the 1960 Olympics if eligible.
However, he could no longer run for Hungary, and wasn"t yet a United States citizen. Thus, there was no country he could compete foreign
Tábori retired from running in 1962. Tábori returned to distance running as a coach in 1967, his training methods based directly on Iglói"s, and has been the coach of San Fernando Valley Track Club since 1973.
He remains a vocal advocate of interval training.