The Queen of Denmark has apologised after stripping four of her grandchildren of their royal titles - but has not reversed the decision.

Queen Margrethe II said she wanted the monarchy in "keeping with the times", that her decision had been a long time coming, and that it would "future-proof" the institution.

But she "underestimated" her family's reaction "and for that I am sorry".

The initial decision was announced last week, to begin next year.

"The titles of prince and princess that they have held up until now will be discontinued," the initial statement said. "Prince Joachim's descendants will thus have to be addressed as excellencies in the future."

Prince Joachim - the younger son of Queen Margrethe - said he was upset by the change.

"It's never fun to see your children being mistreated like that," he told Ekstra Bladet. "They find themselves in a situation they do not understand."

His wife, Princess Marie, said her youngest child had been bullied at school following what she called the "short-notice" announcement.

In an interview, the couple also said Margrethe had not spoken to them since the changes were announced. One grandchild, Prince Nikolai, said his family were "shocked" by the decision.

From the beginning of 2023, Joachim's four children - Prince Nikolai, 23, Prince Felix, 20, Prince Henrik, 13, and Princess Athena, 10 - will be known by the titles Count and Countess of Monpezat instead of Prince and Princess.

The palace said this was a "natural extension" to the Danish monarch's desire to slim down the monarchy.

"Her Majesty The Queen wishes to create the framework for the four grandchildren to be able to shape their own lives to a much greater extent," last week's statement said.

But following what Margrethe described as "strong reactions" to her decision, she apologised in a new statement for underestimating the reaction.

"No one should be in doubt that my children, daughters-in-law and grandchildren are my great joy and pride. I now hope that we as a family can find the peace to find our way through this situation," she said.

Queen Margrethe II's oldest son, Crown Prince Frederik, is first in line to the throne. His four children will keep their titles.

His wife, Crown Princess Mary, supported the Queen, saying "change can be difficult and can really hurt. But this does not mean that the decision is not the right one".

The Danish monarch, 82, tested positive for Covid-19 after attending the state funeral of Queen Elizabeth II - who was her third cousin.