Nicole Kidman appealed to the Sydney media on Thursday for "a little space" as she travels around Sydney with her new baby.

The Oscar-winning actress and her singer husband Keith Urban arrived in her hometown from the United States on Wednesday night with their 4-week-old daughter, Sunday Rose Kidman Urban.

"Keith and I are both appealing to the press ... just to give us a little space so we can walk around Sydney and show the baby our town," Kidman told Sydney radio 2DAY FM.

She said she understood the media interest in the child, "but at the same time, it's our little girl," Kidman said.

"Sometimes when people come right up in your face ... you think: 'Good God, would you do that to anybody else's child?"'

Kidman said the baby looked like Urban with "a bit of a reddish tint" in her hair.

New Zealand-born Urban told the radio station that being a new dad was an "awesome" feeling that only other fathers could understand.