Mekonnen came to prominence at the age of eighteen with a silver medal performance in the 5000 m at the 1998 African Championships in Athletics, finishing behind reigning world champion Daniel Komen. He followed this up with a gold and team silver in the junior race and an individual and team bronze medal in the short race at the 1999 IAAF World Cross Country Championships. He put much of his success down to the help he had received from Haile Gebrselassie, who was his training partner and mentor. He ran a world junior record in the 3000 m in Stuttgart, Germany, but this was never ratified as he did not undergo the doping controls necessary for record purposes. He finished seventh in the 5000 m at the 1999 World Championships in Athletics and closed the year with a 1500 metres gold medal at the 1999 All-Africa Games and a win at the Cross Internacional de Venta de Baños. He set an indoor world record of 8:09.66 in the two miles in Birmingham in February. However, Mekonnen only managed sixth place in the short race at the 2000 IAAF World Cross Country Championships, but again he won the team bronze with Ethiopia. He represented his country at the 2000 Summer Olympics, finishing seventh in the semi-finals of the 1500 metres.