The 90-year-old monarch was addressing the Scottish Parliament at its official opening against the backdrop of Scotland having voted overwhelmingly in favour of remain - 62 per cent against 38 per cent - triggering calls for a second referendum in Scotland for independence from the UK.
"Retaining the ability to stay calm and collected can at times be hard. As this parliament has successfully demonstrated over the years, one hallmark of leadership in such a fast-moving world is allowing sufficient room for which can enable deeper consideration of how challenges and opportunities can be best addressed," she said.
The Queen told the Holyrood chamber that the world was "increasingly complex and demanding" and that developments can take place at "remarkable speed".
Scotland first minister, Nicola Sturgeon, who has pledged to do all she can to maintain Scotland's place in the EU, spoke of the parliament's duty to "enhance and never diminish our place in the world", and said Scotland was determined to remain "open and inclusive".
More From This Section
She said: "Whether we have lived here for generations or are new Scots, from Europe, India, Pakistan, Africa and countries across the globe we are all of this and more. We are so much stronger for the diversity that shapes us."
She added: "Today, as we celebrate this new beginning, let us look forward with hope and a shared determination to work tirelessly for the good of all of Scotland's people - and in doing so, to play our part in a stronger Europe and a better world."
The fifth term of the Scottish Parliament began after May's Holyrood, or Scottish Parliament, elections.