At international level, he represented Brazil on 11 occasions between 1998 and 2000, scoring a single goal; he was a member of the team that finished third at the 1998 CONCACAF Gold Cup.

In his first year, he netted once in 21 appearances, adding another in five UEFA Cup matches; he would be used regularly during his three-year stay, proving himself a threat at set pieces as the capital club lifted the Scudetto in his second season.

Assunção joined Spanish side Real Betis in August 2002, being an undisputed first-choice from the start and scoring several goals from free kicks.

His debut as a Verdiblanco was spectacular, as he netted once in a 4–2 away win against Deportivo de La Coruña through a 40-yarder with his weaker left foot, then proceeded to strike the woodwork on no less than three occasions;[3] he scored eight goals as the Andalusian team finished fourth at the end of the 2004–05 campaign, subsequently qualifying for the UEFA Champions League.

[6] Assunção was selected by manager Luiz Felipe Scolari as one of the club's four "leaders", alongside Marcos, Danilo and Edinho.