- The two are not scheduled to see each other while both are in London.
- The duke's spokesman said the King's "full programme" prevented any meeting.
The Duke of Sussex has attended a service at St Paul's Cathedral in London during a brief visit to the UK.
Prince Harry was speaking at the event to mark the 10th anniversary of the Invictus Games, the sporting competition for injured service men and women he helped found.
Meanwhile, the King, whose cancer treatment is ongoing, met members of the public at a Buckingham Palace garden party a little over two miles away.
The two are not scheduled to see each other while both are in London.
The duke's spokesman said the King's "full programme" prevented any meeting.
A crowd gathered in the sunshine outside St Paul's to greet Prince Harry, the driving force behind the Invictus Games, who smiled and waved from the steps as he arrived.
Once inside, he gave a warm greeting to his uncle, Earl Spencer, who was sitting behind him in the cathedral.
Speaking in the church where his parents were married, Prince Harry gave a Bible reading from Corinthians that emphasised different people have different gifts and strengths.
Another reading from Isaiah talked of stopping “the pointing of the finger, the speaking of evil”.
It was a very traditional service, with hymns, psalms and Bible readings, under the chandeliers and frescoes of the cathedral dome.
There was also an emotional reading of a poem about the positive impact of the Invictus Games by Michelle Turner, captain of the UK’s team in Sydney in 2018.
As he left, Prince Harry got another enthusiastic reception from the crowd outside, who cheered him as he pulled away in a black Range Rover.
He has been in legal battles over security during visits to the UK, but there were lines of City of London police here seeing him safely away.
The duke, who now lives in California, last saw the King in person shortly after his February announcement that he was being treated for an unspecified form of cancer.
The King has since returned to some public duties but is continuing to receive medical care.
On Wednesday he was seen removing his top hat and waving it in the air as a crowd greeted him by singing the national anthem at Buckingham Palace.
Prince Harry is also not expected to meet the Prince or Princess of Wales - who is also being treated for cancer - while in the UK.
On Tuesday, a spokesperson for the duke said: "In response to the many inquiries and continued speculation on whether or not the duke will meet with his father while in the UK this week, it unfortunately will not be possible due to His Majesty's full programme.
"The duke of course is understanding of his father's diary of commitments and various other priorities and hopes to see him soon."
On Tuesday, the duke attended an Invictus Games summit in London, where he told delegates: "Sometimes you... look back and go 'Look at what we've done'.
"But also given the state of the world, there is so much more to do and I think a lot of uncertainty - but what we've created is a global community."
Prince Harry is not being joined by the Duchess of Sussex for this visit, but his wife is scheduled to meet him in Nigeria, where he is due to travel after his stop in London.
The couple were invited by Nigeria's chief of defence staff after they met at the Invictus Games held last year in Germany.