The duo were embroiled in a brief war of words towards the end of last year, with Messi's alleged request for a new contract the topic of conversation.
Messi, who has recently returned to action following a hamstring injury, signed a new deal in February, but is reportedly not the highest earner at the club following the close-season signing of Brazil international Neymar.
However, Faus has now backed down, claiming only the best will do for Messi.
"He’s the best in the world and he’s been that for the last five years, whatever the awards say," said Faus at the unveiling of plans to redevelop the club's Camp Nou stadium. "He’ll continue playing for Barca .
"I would second the President’s words – he’s the best player in the world and he deserves the best economic treatment.
"It (the row) is something which is happily resolved now, as Leo has said on a number of occasions. There was no bad intent meant on either side."
Barcelona currently sit joint top of La Liga, level on points with Atletico Madrid.
