David Cameron said the birth of his fourth child, a baby girl born early and delivered by Caesarean section, was "absolutely thrilling, really exciting".
The Prime Minister's wife Samantha went into labour in the early hours and gave birth at the Royal Cornwall Hospital in Truro.
The baby, weighing 6lb 1oz, had been due next month but took the Camerons by surprise while they were holidaying in Cornwall.
A beaming Mr Cameron told reporters the baby did not have a name yet, but said it would "have to have something Cornish in the middle".
"It was very exciting, we were on holiday, thought we were going to get through the holiday and then have a baby, and then it just seemed to kick off a bit quickly," the Prime Minister said.
"We woke up this morning and thought she was having contractions and it was all beginning to get going, so we thought we would come to the hospital just to get everything checked out, and then things sort of sped up and it all happened very very quickly and the baby popped out at about 12 o'clock.
"They seemed to be doing fine and my job was to make the toast and the tea, things like that, but it's absolutely thrilling, really exciting and it's just lovely they are both doing so well."
Mr Cameron said the early birth had been "a bit of a shock".
He said: "It was a bit of a shock. I always thought it was possible because Samantha's have tended to come a bit early
"She had been having contractions for the last couple of days on and off and just sort of thought this was time to come to the hospital and check out, see if everything was fine, and the next thing we knew we were all getting into the gear and baby was coming out."
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