Florence Rose Endellion did not appear to be disturbed by the banks of photographers and camera crews on the opposite side of Downing Street.
She was wearing a white shawl that was crocheted by Birmingham well-wisher Jane Fraser-Cross, who had sent it to the Camerons as a gift for their new daughter.
Mr Cameron joked that he had changed “hundreds” of nappies since Florence was born last week at the Royal Cornwall Hospital in Truro weighing six pounds one ounce.
Mrs Cameron had gone into labour early during a family holiday. The prime minister is currently taking Endellion was chosen as a name after the village St Endellion on the north Cornish coast.
In a statement, the prime minister said: “Samantha and I would like to take this opportunity to thank everyone for their kindness and generosity since the birth of baby Florence.
“We have been really, really touched by all the people who have offered their warm congratulations, and by the many cards, gifts and flowers that we have received.”