Suleiman broke into the global elite at the age of nineteen later that year, taking a gold medal at the 2002 Asian Athletics Championships.

Another of his brothers (Nasser Suleiman) won a 5000 metres medal at the same competition and Abdulrahman said of his 1500 m win "I am proud to have kept up a 12-year-old family tradition".

[2] The performance at the continental championships earned him a 1500 m place on the Asian team at the 2002 IAAF World Cup.

His brother Mohamed was the 1992 champion of the competition, but the younger Suleiman did not scale such heights and finished in seventh place.

At the 2005 Asian Athletics Championships he completed a Qatari 1–2 in the 1500 m with Majed Saeed Sultan and Suleiman's runner-up time of 1:44.73 was a new personal best.