In a video message, she said many people hoped the "time for words has now moved to the time for action".
She urged them to act "for our children and our children's children" and "rise above the politics of the moment".
The Queen added she took "great pride" in how her "dear late husband" Prince Philip promoted environmental issues.
The 95-year-old monarch had been scheduled to attend the United Nations conference in Glasgow. But she pre-recorded her address last week at Windsor Castle after being advised to rest following medical checks.
The 95-year-old monarch underwent preliminary medical checks in hospital last Wednesday after cancelling a visit to Northern Ireland.
She resumed public engagements on Tuesday, by meeting ambassadors via video link from Windsor Castle.
Buckingham Palace said she "regretfully" decided not to attend a reception at the summit.
In images released on Tuesday, the Queen was seen smiling on camera as she greeted the South Korean and Swiss ambassadors, who were speaking to her from Buckingham Palace.
In a video call with frontline workers, Prince William offered his congratulations and described the programme as "tremendous" saying it didn't "just happen".
Staff joked they had been "thinking and dreaming" of vaccines all day and night with some describing working seven-day weeks.
The duke also praised his grandparents, the Queen and the Duke of Edinburgh, for stepping up and getting the vaccine.
While celebrations would be different for many this year, she said: "We need Easter as much as ever."
Referencing the tradition of lighting candles to mark the occasion, she said: "As dark as death can be - particularly for those suffering with grief - light and life are greater."
It comes as the number of coronavirus deaths in UK hospitals reached 9,875.
Speaking from Windsor Castle, the Queen said many religions had festivals celebrating light overcoming darkness, which often featured the lighting of candles.
She said she was "entirely supportive" of their desire for a new role but "would have preferred" them to remain full-time working royals.
She expected final decisions to be made in the coming days, she said.
Senior royals have been in talks about Prince Harry and Meghan's role after they said they wanted to "step back".
In a statement, the Queen said the talks at Sandringham, which also involved the Prince of Wales and the Duke of Cambridge, had been "very constructive".
Palace officials told the BBC that Prince Harry, the Duke of Cambridge and the Prince of Wales will all attend, while Meghan is expected join the discussion over the phone from Canada.
The Sussexes say they plan to step back as senior members of the Royal Family.
There is no suggestion a conclusion will be reached at the meeting.
But BBC royal correspondent Jonny Dymond said it is hoped that the talks will produce a "next step" on the way to defining the couple's new relationship with the Royal Family - in line with the Queen's wish to find a solution within days.
BBC royal correspondent Nicholas Witchell said Her Majesty had been in touch with the Prince of Wales and the Duke of Cambridge on Thursday.
They directed senior staff to work with the Sussex household and government.
It comes as the Royal Family was said to be "hurt" at the couple's statement.
Prince Harry and Meghan did not consult any other royal about making their personal statement, palace sources have told BBC royal correspondent Jonny Dymond.
