Following some impressive performances for the Italian youth side, Riva made his senior international debut with Italy at the age of 20, on 27 June, 1965, in a 2–1 friendly defeat against Hungary, coming on for the injured Ezio Pascutti in the eighth minute; he was the first Cagliari player to be capped at senior international level. His international career took off to a difficult start, as his performance in his second appearance for Italy, a 0–0 friendly draw against France in Paris on 19 March 1966, was criticised by noted journalist Gianni Brera, who initially described Riva as a "one-footed" and "incomplete player". He was subsequently controversially excluded from the 22-man 1966 FIFA World Cup squad, although he was still brought to England by manager Edmondo Fabbri, along with Mario Bertini, as an additional reserve, in order to gain experience with the national side; Italy were eliminated in the first round of the tournament. After breaking both his left tibia and fibula in his third international appearance, a 1–1 friendly home draw against Portugal on 27 March 1967, Riva returned to the national team as a starter seven months later, and finally scored his first goal for Italy in his fourth international appearance, a 5–0 home win over Cyprus on 1 November 1967, in a UEFA Euro 1968 qualifying match, later completing a hat-trick in the same game. Riva was a member of the Italian side that won the 1968 European Championships on home soil under manager Ferruccio Valcareggi; after recovering from a leg injury, he returned to the starting line-up and scored the opening goal in the twelfth minute of the final replay in Rome on 10 June, which ended in a 2–0 victory over Yugoslavia; Riva was named to the Team of the Tournament for his performance during the match.