The 76-year-old Scottish actor, who has previously spoken of his support for the SNP, also talked about his view on the country’s independence as he appeared on BBC One’s Sunday With Laura Kuenssberg programme.
He told the political broadcaster: “I’m very, very proud of Scotland for doing the gender identification Act, because I think that’s long needed and it’s a debate that has to happen.
“And I do question the 16 thing, but that’s my own personal feeling, but I do feel we need to address that and I think that’s absolutely right.”
Cox was speaking just after Labour leader Sir Keir Starmer said he had “concerns” over 16 being too young to decide to change gender.
The Gender Recognition Reform (Scotland) Bill, passed by MSPs, approved reforms which would allow trans people to obtain a gender recognition certificate (GRC) without the need for a medical diagnosis.
The Bill will also allow 16 and 17-year-olds to apply for a GRC for the first time, and would reduce the amount of time a person has to live in their acquired gender before they can be granted the document.
Cox also said he thought people are being a “bit high and mighty” about Harry Potter author Rowling’s views on transgender rights.
He added: “I don’t like the way she has been treated.
“Actually, I think she’s entitled to her opinion, she’s entitled to say what (she feels), as a woman, she’s very much entitled to say what she feels about her own body.
“So I do feel that people have been a bit high and mighty about their attitude towards JK Rowling, quite frankly.”
He also said Britain needs to “rethink” itself as a nation as the “economy is shrunk” and there has been a loss of power in the world.
Cox said: “I think since the passing of our wonderful Queen, I think we’ve had to consider the monarchy and we’re seeing it in relationship to what has been going on in the book, Spare, the Harry situation, so there’s a lot of massive rethinking that needs to be done.”
In the Duke of Sussex’s memoir he expresses his frustration at being the “spare to the heir”, his anger at the UK media, his unresolved trauma over the death of his mother, his mental health struggles, his lonely life before meeting Meghan, and the breakdown of his family relationships.
Cox also called First Minister Nicola Sturgeon “very canny” as she tries to get another referendum on Scottish independence.
On Scotland leaving the UK, Cox said: “My relationship to Scottish independence is quite different and I don’t believe this is a break-up of the United Kingdom.
“I think it could be a different kind of united. I would like to see the United Federation where each country comes into its own, and its sense of autonomy and can contribute as a result to a United Federation, where everybody comes together.
“At the moment, it’s top heavy, because it’s very self-orientated and I feel that that needs to change, that needs to shift.”