Prince William's pregnant wife Kate was feeling better on Tuesday after a second day of hospital treatment for acute morning sickness, palace officials said.
William spent most of the day at his wife's bedside as congratulations poured in from around the world after Monday's announcement that the Duke and Duchess of Cambridge, both 30, are expecting their first child -- a new royal heir.
"The Duchess of Cambridge is continuing to feel better," a spokesman for the couple's office at St James' Palace said.
"She and the Duke are immensely grateful for the good wishes they have received."
He added that Kate would remain at the private King Edward VII Hospital in central London and continue with treatment for hyperemesis gravidarum, a severe form of morning sickness that affects about one in 200 pregnant women.
News of the pregnancy has ended feverish speculation about a new heir that began immediately after their lavish wedding in April 2011.
The baby will be third in line to the throne regardless of whether it is a girl or a boy, after a historic agreement among the 16 Commonwealth realms last year to end the centuries-old practice of male primogeniture.
Britain said on Tuesday that it received formal consent for the new laws from the other realms on the very day the pregnancy was announced, in what Deputy Prime Minister Nick Clegg called a "wonderful coincidence".
William, the second in line to the throne after his father Prince Charles, visited his wife in hospital following her admission on Monday afternoon and spent more than six hours with her on Tuesday.
Wearing a purple jumper over a shirt and jeans, he emerged from the hospital at 5:45 pm (1745 GMT) and smiled at the waiting media before being driven away.
St James's Palace has said Kate is still at the "very early stages" of pregnancy -- likely less than 12 weeks -- and it is thought the news was released because her admission to hospital would have made her condition public.
Hospitalisation is needed in severe cases of hyperemesis gravidarum to treat dehydration with intravenous fluids for a few days, as it is impossible to keep fluids down.
Kate is expected to stay in hospital for several days and will then require a period of rest, a palace spokeswoman said, adding that her public engagements have been cancelled for the next week.
The diagnosis has meanwhile sparked speculation that Kate may be expecting twins, as experts say the condition is more common with a multiple pregnancy.
Palace officials said the royal couple only "recently" became aware that Kate was pregnant although there has been speculation for months, fuelled by images of the duchess sipping water instead of wine at official dinners.
She showed no sign of being ill at her most recent public engagement on Friday, when she displayed her hockey skills at her old primary school, wearing high-heeled boots and an Alexander McQueen tartan coat.
There was reportedly a rush to inform members of the royal family of the news before the public announcement.
Queen Elizabeth II, her husband Prince Philip, Charles and his wife Camilla were said by the palace to be "delighted", as were Kate's parents, Carole and Michael Middleton.
William's brother Prince Harry, 28, who will be bumped down to fourth in the line of succession by the new arrival, was reportedly informed by email in Afghanistan, where he is deployed as an Apache attack helicopter pilot.
News of the pregnancy sparked huge excitement in the British press as well as a frenzy of Internet speculation about what the child will be called and what it will look like, with numerous bizarre mock-up photographs being circulated.
Prime Minister David Cameron, who had his fourth child in 2010, led the congratulations by saying the royal couple would make "wonderful parents".
US President Barack Obama and his wife Michelle, who met William and Kate during a state visit to Britain last year, also sent their congratulations.
Australian Prime Minister Julia Gillard said the news "is going to bring joy to many around the world", while her New Zealand counterpart John Key said it was "fabulous".
New Zealand had led the push for Commonwealth realms to scrap the laws barring first-born daughters from inheriting the throne.
MORE ON THE ROYAL BABY
Prince William and Kate Middleton’s baby could be named after Princess Diana
Daddy-to-be Prince William could name his little princess Diana, in loving memory of his mother, according to one expert.
Royal Author Phil Dampier said that he would be “astonished” if Kate and William did not use Princess Diana’s name for their first-born, if they were to have a royal baby girl, the Mirror reported.
Diana was one the most popular choice and Dampier believes the couple will no doubt be thinking about some sort of tribute to Princes William and Harry’s late mother, who died in a car crash in Paris in 1997.
“I think Diana’s influence will be very strong. Kate will surely have asked William about his upbringing and on their engagement Kate spoke about her regret at not meeting Diana and how she found her an inspiration,” Dampier said.
“I’m sure she will be looking at what Diana did as a mother and learning from her. I would be utterly astonished if Diana didn’t make up some part of the name should the baby be a girl."William missed her at the abbey when he wed Kate – she is always in his mind," he added.
William-Kate’s baby to inherit throne regardless of gender
The royal baby due next year to the Duke and Duchess of Cambridge will ultimately accede to the throne regardless of its sex after changes in the rules of Royal succession, according to ministers.
In a break with more than 300 years of English constitutional tradition, laws that would have passed the Crown to the oldest male heir will not apply, the Telegraph reported. HEIR APPARENT
Kate Middleton, Duchess of Cambridge expecting twins?
The Duchess of Cambridge, who is expecting her first child with Prince William, maybe pregnant with twins, according to reports.
Kate, who has been admitted to the King Edward VII Hospital in London after she got ill while staying with her parents in Bucklebury, Berkshire, is suffering from hyperemesis gravidarum, a condition that is more often experienced by women expecting twins, the Telegraph reported.
(With additional inputs)