The Princess Royal is "fine", her husband has said, after she sustained a minor head injury and concussion thought to have been caused by a horse.
Vice Admiral Sir Tim Laurence visited Princess Anne, 73, at Southmead Hospital, Bristol, for two hours on Tuesday.
As he left the main entrance of Southmead Hospital, Bristol, at about 14:00, he said: "She’s doing fine, slow but sure."
It is the second day in hospital for the princess, after she was admitted on Sunday following an accident on her Gloucestershire estate.
Asked if he had taken anything for the princess, Sir Tim said: "Just a few little treats from home."
Princess Anne is expected to make a full recovery but she will miss the state banquet with the Emperor and Empress of Japan later and her trip to Canada this week has been postponed.
The King has sent "his fondest love and well-wishes" to the princess "for a speedy recovery", while Prime Minister Rishi Sunak and Labour leader Sir Keir Starmer have also sent their best wishes.
The Princess Royal was injured on Sunday evening when she was out walking on her estate and horses were nearby.
It is understood the princess has not been able to recall the details of what happened on Sunday evening due to her concussion.
Her medical team suggested her head injury is consistent with the type of impact from a horse’s legs or head.
Emergency services were called to the estate and the princess was taken to hospital.
Her husband Admiral Sir Tim Laurence and her daughter Zara and son Peter were on the estate at the time.
The princess is conscious and is expected to stay in hospital until later this week "as a precautionary measure for observation", a Buckingham Palace statement said on Monday.
Southmead is an NHS hospital, part of the North Bristol NHS Trust, and has a number of major specialities, including neuroscience.
A Buckingham Palace spokesman said: "Her Royal Highness is recovering well, is in a comfortable condition and is being kept in hospital as a precautionary measure for further observation."
The spokesman added: "On doctors’ advice, Her Royal Highness’s engagements for the week ahead will be postponed. Her Royal Highness sends her apologies to any who may be inconvenienced or disappointed as a result."
According to the NHS, concussion can be the result of a "temporary injury to the brain caused by a bump, blow or jolt".
It can cause forgetfulness, tiredness and a lack of concentration and can take a couple of weeks before a full recovery.
This week, the princess had a series of events planned, including the Japanese state visit, with other engagements scheduled in Scotland, Hampshire and Gloucestershire.
The hospitalisation of Princess Anne is the latest health problem facing the Royal Family.
King Charles and the Princess of Wales both have had a cancer diagnosis this year, limiting their public engagements.
Meanwhile, Emperor Naruhito and Empress Masako of Japan have begun a three-day state visit to the UK.
They received a ceremonial welcome and a carriage ride up the Mall, with a state banquet being hosted later by King Charles III at Buckingham Palace.
But because of the general-election campaign, the Japanese royal couple will not make a trip to Downing Street.