Despite leading the Catalan outfit into the quarter-finals of the Champions League and into the Copa del Rey final, Martino has come under criticism this season.
Various reports have suggested that Martino could be forced out of the Camp Nou this summer, but the Argentine has claimed that he will remain at the helm.
"It's completely true what the president said," he told reporters at a press conference.
"I always fulfil my contracts. There's nothing that I'm doing that's not in what the contract says or when we speak face to face. I'm a man of my word."
Barcelona welcome Celta Vigo in the league on Wednesday.