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."
They 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.
Londoners react to news of upcoming new royal baby
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.