Boris Johnson believes the Duke and Duchess of Cambridge's royal train tour is a "welcome morale boost", No 10 said, after Downing Street officials initially refused to say it complied with coronavirus restrictions.
Concerns about the tour have been raised by Welsh and Scottish ministers at a time when many parts of the UK are subject to strict rules to control the spread of Covid-19.
The Prime Minister's official spokesman said the tour was a "matter for the palace".
Challenged on whether the royal couple had complied with the rules, the spokesman said: "I'm making the general point that we have set out the regionalised tier system that is now in place and the guidance that we are asking people to abide by."
In response to a suggestion that No 10 was refusing to give its backing to the couple's trip, the spokesman said: "I would point you towards the palace."
But an hour after the comments in a Westminster briefing, a statement issued by No 10 confirmed Mr Johnson's support.
A No 10 spokesman said: "The PM is delighted to see the warm reception the Duke and Duchess of Cambridge have received on their hugely valuable train tour of England, Scotland and Wales.
"The tour will be a welcome morale boost to frontline workers who have done so much during the pandemic."
With the Welsh Samba band playing within the castle walls, The Duke and Duchess were able to hear how they have been supported during the pandemic through the UK Government's Culture Recovery Fund.
— The Duke and Duchess of Cambridge (@KensingtonRoyal) December 8, 2020
The clarification of No 10's position came after Welsh Health Minister Vaughan Gething said he would prefer it if "no-one was having unnecessary visits".
Mr Gething said he was not "particularly bothered or interested" when asked during BBC Radio 4's Today programme if he thought the couple should still travel to Wales.
But he said William and Kate's visit should not be used by people as an "excuse" to say they are "confused" about coronavirus regulations.
Mr Gething echoed the sentiment of Scotland's First Nicola Sturgeon, who suggested the duke and duchess travelled to Edinburgh on Monday despite their office being made aware of restrictions for those wanting to cross the border.
The couple began their trip to Wales by visiting Cardiff Castle, where they met university students and heard about the mental health challenges they faced during the pandemic.
As they chatted, William and Kate admitted they were struggling with Christmas plans, suggesting they had yet to decide who to spend the festive period with.
"It is so difficult, we are still trying to make plans. It's difficult to know what to do for the best," said the duke.
The duke and duchess have been touring the country thanking key and frontline workers and communities for their efforts during the pandemic.
At Cardiff Castle, William and Kate, who wore a red Alexander McQueen coat, met students from Cardiff University, Cardiff Metropolitan University and the University of South Wales, as they unwrapped their Secret Santa gifts to one another.
The visit coincided with Christmas At The Castle, a festival of seasonal activities there throughout December.
William and Kate browsed some of the Christmas stalls and toasted large marshmallows over a fire.
Touching one of the sticky sweet treats with her gloved hand, Kate laughed and said: "I'm going to have that marshmallow on my fingers all day."
Lily Faulkner, 21, a second year politics and international studies student at Cardiff University, said: "They were trying like the rest of us to make Christmas plans with their family and still weren't 100% sure of what they were going to do or where they were going to be."
William and Kate's tour also took them to Cleeve Court Care Home in Twerton, Bath, a chance to pay tribute to the efforts of care workers across the country.