In return, UEFA will consider loosening rules which prohibit the display of any flags or banners with political connotations, saying such regulations needed to evolve to respect "freedom of expression".
UEFA said in a statement that it would set up a working group to review its disciplinary framework so that clubs are punished only "in circumstances and cases where the majority of reasonable people think that a sanction should be imposed".
Barcelona appealed to the Court of Arbitration for Sport (CAS) after they were twice fined over the flags, known as esteladas, last year.
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UEFA fined them 30,000 euros (25,231 pounds) after supporters waved the flags during the 2015 Champions League final in Berlin and another 40,000 euros for similar incidents in a tie against Bayer Leverkusen.
The disciplinary board ruled the club had breached regulations which prohibit "the use of gestures, words, objects or any other means to transmit any message that is not fit for a sports event, particularly messages that are of a political, ideological, religious, offensive or provocative nature".
On Monday, UEFA said Barcelona had recognised that disciplinary bodies had little scope to depart from established rules which had to be enforced "including with respect to the existing prohibition of political type messages at football matches."
However, the organisation added that the rules were not "set in stone".
"They can, and should, evolve to reflect the nature of the society in which we live, where freedom of expression is generally a value to be supported and cherished," said UEFA.
(Editing by Tony Jimenez)
