The Argentinian was last week reported to be considering cutting short his reign with the Spanish champions after coming in for criticism as a result of Barca losing top spot in La Liga.
Martino signed a two-year contract when he was appointed as Tito Vilanova's successor last July, and the 51-year-old has denied speculation that his tenure could come to a premature end.
Barca president Josep Maria Bartomeu revealed earlier on Tuesday that Martino had given assurances that he will not quit at the end of the current campaign.
And the coach himself stated "I always respect my contracts" at a press conference on the eve of Wednesday's Liga clash with Real Betis.
Lionel Messi's hat-trick in Sunday's enthralling Clasico at the Bernabeu secured a 4-3 victory for the champions as an intriguing title race continues to throw up twists and turns.
Martino is determined to ensure his side kick on following that stunning victory over title rivals Real Madrid by overhauling the one-point gap between themselves and Real and Atletico Madrid at the top of the table.
He added: "It is important for us to be in the right frame of mind for this run-in to the end of the season, and we are still competing on all three fronts (Barca are also in the UEFA Champions League quarter-finals and Copa del Rey final) and finding our form, so it's all positive.
"We have to make the most of what we achieved at the weekend, because it has put us back in contention for the league title."
