The Queen was “on very good form” during her weekly briefing with Boris Johnson, the prime minister has told ITV News.
His comments came after the 95-year-old monarch was told to rest for another two weeks by her doctors.
Her Majesty has been instructed by physicians to only undertake “desk-based duties” and will not be permitted to attend public events.
The medics' orders came after the Queen underwent tests in hospital last week and cancelled a two-day trip to Northern Ireland at the last minute.
Amid public concern for the Queen, the prime minister told ITV News there was no cause for worry and said the public must "respect" her need to step back from some duties for the time being.
"Everybody wishes her all the very best"
Speaking in Rome on Saturday, where the PM has travelled for the G20 summit, he said: "I spoke to Her Majesty as I do every week as part of my job and she was on very good form.
“She has been told by her doctors that she has got to rest and I think we have got to respect that and understand that.
"Everybody wishes her all the very best.”
Despite ruling out attendance at the Festival of Remembrance at the Royal Albert Hall on November 14, the Palace said the head of state has the “firm intention” of leading the nation in honouring the country’s war dead on Remembrance Sunday the next day.
And on Friday afternoon, Her Majesty recorded a speech to play to world leaders at the COP26 meeting in her absence.
There will be concern for the Queen given her advanced years - and following her recent appearance walking with the aid of a stick - but medics see the period of rest as a sensible precaution.
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In a statement on Friday, Buckingham Palace said: “Following on from their recent advice that the Queen should rest for a few days, Her Majesty’s doctors have advised that she should continue to rest for at least the next two weeks.
“The doctors have advised that Her Majesty can continue to undertake light, desk-based duties during this time, including some virtual audiences, but not to undertake any official visits.
“Her Majesty regrets that this means she will be unable to attend the Festival of Remembrance on Saturday, November 13.
“However, it remains The Queen’s firm intention to be present for the National Service of Remembrance on Remembrance Sunday, on November 14.”
The Queen appeared cheerful and in good humour when she hosted a virtual presentation ceremony on Thursday, awarding the Queen’s Gold Medal for Poetry 2020 to poet David Constantine.
It was announced last Wednesday the Queen had “reluctantly” accepted medical advice to rest and cancelled her trip to Northern Ireland that was scheduled to begin that day.
But it later emerged she had stayed overnight in hospital when The Sun newspaper reported the monarch had been admitted to King Edward VII’s Hospital in central London on Wednesday.
Buckingham Palace confirmed the head of state had undergone “preliminary investigations” during her first overnight stay at a medical facility in eight years.