Throughout his career, the tennis star has preferred to be known as Scottish, but has chosen to remain neutral on his daughter’s nationality.
The 28-year-old, from Dunblane, and wife Kim, from East Sussex, welcomed the arrival of their daughter Sophia Olivia on 7 February.
As Great Britain prepared to begin their defence of the Davis Cup against Japan in Birmingham, Murray told 5 News that Sophia was neither Scottish nor English.
“I believe she’s British,” he said.
Asked how he was coping with the challenge of juggling life as British number one and being a first-time father, he said: “It’s been great so far, obviously this week I haven’t seen her (Sophia) for a few days so that’s been tough.
“I’m just trying to keep my focus when I’m on the court on my tennis.
“Obviously when I’m away from the court my thoughts are back home and trying to speak to Kim as much as possible, stay in touch, but it’s not easy being away for the first few days when she’s so young.”