Mauresmo admitted she had felt emotional listening to his words but also surprised. She said the idea of a woman coaching a man had not been an issue she had discussed with Murray.
"I appreciated the gesture," she said. "I think he probably also did it for himself because at every press conference since Wimbledon last year, he answered questions about me and whether he had made the right decision to appoint me. He had probably had enough of that.
"It's always better to show something with results than respond with words - and he's showing those results right now."
Did Mauresmo believe she had been brave to take the job as Murray's coach?
"When it happened, not really, but looking back now, yes," she said. "We were really on the same page as to why he was asking me to coach him. I thought I could really help him in these different areas that he was looking to improve, so it was not an issue for me.
"Then when I heard or read a few of the comments and stuff [about him appointing a female coach], I thought, 'Wow, it's not that easy'. In terms of where society is right now, it's still not that easy. Hopefully it will make things easier now.
"He was also brave, but he's not scared of those things. He has his own ideas and beliefs and he's pretty strong about those. I think he was brave, but I also believe he was just moving forward with what he thought was the best thing to do."
Murray said the end of last year had been a difficult time for Mauresmo. Despite his success in qualifying for the season-ending ATP World Tour Finals, questions were still being asked about the Frenchwoman.
His crushing defeat to Roger Federer in his final match of the year did nothing to dispel those doubts, although Murray pointed out he'd had few opportunities to work with Mauresmo, who started coaching him just before Wimbledon.
"There's no reason for her to be criticised, because I only spent two weeks training with her, one week before the US swing and one week before the US Open, when it was tough to work on things," he said.
"It doesn't matter what anyone else thinks, it's what I think - and I believe in her. When we talk about my game, we completely agree on the things I need to work on, the way I need to play the game. So that's a good start.
"After that, it's just about practising it, working on it and then putting it into effect on the match court. She's done a very good job. She's a very good coach." The Independent
