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The Queen places a wreath in remembrance of the victims of the Sept. 11, 2001, attacks on the World Trade Center site in New York. ((Fred R. Conrad/Associated Press))

Queen Elizabeth placed a wreath of flowers at a site of the Sept. 11 attacks Tuesday and chatted with victims' families and first responders, minutes after using her first visit to New York in more than three decades to praise the UN for promoting peace and justice.

The 84-year-old monarch braved 38 C heat in a 15-minute visit to the World Trade Center site after challenging the United Nations to spearhead an international response to global dangers.

Near the footprint of the trade centre's south tower, she placed a wreath of red peonies, roses, lilies and black-eyed Susans on a wooden riser at the site.

'She's beautiful. She looks like she could be anybody's grandmother.' —Debbie Palmer, 9/11 widow

Dressed in a two-piece white, blue and beige print dress with a ruffled hem and a matching brimmed champagne-coloured silk hat with flowers, the Queen smiled and nodded at a phalanx of dignitaries, relatives of Sept. 11 victims and first responders gathered to meet her.

The Queen "just was asking me about that day, and how awful it must've been," said Debbie Palmer, whose husband, battalion fire chief Orio Palmer, was killed on Sept. 11.

"She said, 'I don't think I've ever seen anything in my life as bad as that. And I said, 'Let's hope we never do again.' "

Palmer said, "She's beautiful. She looks like she could be anybody's grandmother.

"And she looks like royalty, because we're all sweating and she was quite the lady — no sweat whatsoever! Her lipstick was just so."

The Queen left the site in a motorcade to visit the British Garden of Remembrance, built to honour the 67 Britons killed in the 2001 attack. She cut a ribbon to officially open the memorial.

Earlier Tuesday, she challenged the UN to promote prosperity and dignity for the world's inhabitants.

"In my lifetime, the United Nations has moved from being a high-minded aspiration to being a real force for common good," the Queen told diplomats from the 192 UN member states. "That of itself has been a signal achievement.

"But we are not here to reminisce. In tomorrow's world, we must all work together as hard as ever if we are truly to be United Nations."

Speaking as queen of 16 UN member states and head of a commonwealth of 54 countries with a population of nearly two billion people, Elizabeth recalled the dramatic changes in the world since she last visited the United Nations in 1957, especially in science, technology and social attitudes.

But she also praised the UN's aims and values, which have endured — promoting peace, security and justice; fighting hunger, poverty and disease; and protecting the rights and liberties of every citizen.

"For over six decades the United Nations has helped to shape the international response to global dangers," she said. "The challenge now is to continue to show this clear … leadership while not losing sight of your ongoing work to secure the security, prosperity and dignity of our fellow human beings."

Royal sendoff from Toronto

The royal couple had left Toronto Pearson International Airport just after 1 p.m. ET, as Gov. Gen. Michaëlle Jean, Prime Minister Stephen Harper and other dignitaries looked on.

They shook hands with Jean and Harper before climbing the stairs to the waiting Canadian Forces plane, then turned and waved a final time before boarding.

After her departure, Harper said he was "delighted and honoured" to have welcomed the Queen to Canada.

"The royal tour gave Canadians, and Canadian youth in particular, an opportunity to reacquaint themselves with their traditions, history and institutions — core elements, one and all, of our Canadian identity," Harper said in a statement.

The Queen and Prince Philip departed for London from John F. Kennedy International Airport at around 7 p.m. ET Tuesday.

With files from CBC News