Mr Brown and his wife have two sons, aged two and four
Gordon Brown has spoken of his "struggle" to raise a family while being prime minister.
He told ITV1's This Morning that the "the most important thing is being a good father and a good parent".
Mr Brown also said he hoped his youngest son Fraser, who has cystic fibrosis, could one day become a football or rugby player.
He was "doing well" and the family was "very hopeful" about the future, the prime minister added.
Mr Brown's comments come after poor local election results for Labour last week, which some observers blamed on his inability to connect with voters.
He admitted at the weekend that he was a more "private person" than predecessor Tony Blair.
But Mr Brown told This Morning presenter Fern Britton that his two sons helped him keep politics in perspective.
He said: "The most important thing is being a good father and a good parent, as you know, and nothing I do will neglect my children.
"It has been such a struggle to have two young healthy children, so it is really important to me."
Mr and Mrs Brown's first child, Jennifer Jane, was born prematurely in 2001 and died aged 10 days.
They have since had two sons, John, aged four, and Fraser, who will be two in July.
Mr Brown said: "He [Fraser] is doing well, and although he has got cystic fibrosis he is really doing well and we are very hopeful.
"You know, for the condition you have got to do more sport, you have got to do running, you have got to do keep fit - you have got to do all these things.
"I want him to be a rugby player or a football player."
Cystic fibrosis is a life-threatening inherited disease which disrupts the way the digestive and respiratory systems work.