Family members have visited the Duke and Duchess of Cambridge and their baby daughter at Kensington Palace.
According to the BBC, the Prince of Wales and Duchess of Cornwall spent more than an hour with their new granddaughter.
The Duchess of Cambridge's parents, Michael and Carole Middleton, and her sister Pippa also met their newest relative.
The name of the duke and duchess's second child - sister to Prince George - could be announced later.
The princess, who is fourth in line to the throne, was delivered at 8.34 a.m. BST on Saturday at St Mary's Hospital in London, and weighed 8lbs 3oz (3.7kg).
Tower Bridge was among several London landmarks lit up in pink in her honour.
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The Cambridges will spend the next few days at Kensington Palace; afterwards they are expected to travel to their country home Anmer Hall on the Queen's Sandringham estate in Norfolk.
Bookmakers say Charlotte and Alice have emerged as the favourite names for the princess, followed by Olivia, Victoria and Elizabeth.
Meanwhile, almost all of the UK's national newspapers have given over the entire front pages of their Sunday editions to the birth and a photograph of the new princess.