Suarez, Philippe Coutinho, Ivan Rakitic, Samuel Umtiti, Yerry Mina and Thomas Vermaelen all trained for the first time since the World Cup.
Lionel Messi, Marc-Andre ter Stegen, Gerard Pique, Sergio Busquets, Ousmane Dembele, Jordi Alba and Sergi Samper were also involved as the Spanish champions were put through their paces in a light session at their Ciutat Esportiva Joan Gamper base.
Messi and Suarez, who scored 59 La Liga goals between them last season, stood side by side for a briefing before the players were made to work.
Sprinting drills and a passing exercise were on the agenda as Barca’s big hitters were eased back into the swing of things.
Barca entered the International Champions Cup this summer with a youthful side who drew 2-2 with Tottenham before losing to Roma and Milan in the United States.
It is expected that some of the club’s main men will feature in the Spanish Super Cup against Sevilla on Sunday.
Barca then contest the Joan Gamper Trophy against Boca Juniors on August 15, before their La Liga campaign kicks off three days later when Alaves visit the Nou Camp.