United Nations (CNN) -- Britain's Queen Elizabeth II on Tuesday addressed the United Nations for the first time in more than 50 years, saying she has "witnessed great change, much of it for the better" since her previous speech there in 1957.

Later Tuesday, the queen visited ground zero to lay a floral wreath at the site of the September 11, 2001, terror attack. In a separate event in New York, she cut the ribbon to officially open the Garden of Remembrance for British citizens killed in the attack.

The seven-minute speech to the U.N. General Assembly touched on her first visit decades earlier, when she was a young monarch and the United Nations itself was a young organization.

"When I was first here, there were just three United Nations operations overseas," the queen noted. "Now over 120,000 men and women are deployed in 26 missions across the world."

She spoke of the importance of leadership and how critical the role of the United Nations continues to be in upholding human rights in the 21st century.

"You have helped to reduce conflict, you have offered humanitarian assistance to millions of people," she said, adding that the United Nations has been "deeply committed to tackling the effects of poverty in many parts of the world."

Despite such efforts, she said, "so much remains to be done," citing the struggle against terrorism and the response to climate change.

The queen called for special attention to the "risks facing smaller, more vulnerable nations," many of which belong to the 54-member Commonwealth of Nations that she heads.

"I know of no single formula for success," she said. "But over the years I have observed that some attributes of leadership are universal and are often about finding ways of encouraging people to combine their efforts, their talents, their insights, their enthusiasm and their inspiration to work together."

The United Nations "has helped to shape the international response to global dangers," she said, adding that the challenge is to continue to show such leadership without losing sight of "your ongoing work to secure the security, prosperity and dignity of our fellow human beings."

"It is my hope that when judged by future generations, our sincerity, our willingness to take a lead, and our determination to do the right thing will stand the test of time," she said.

However, she added, her speech was not "to reminisce" but instead to focus on the hard work required ahead "if we are truly to be united nations."

In welcoming the queen, U.N. Secretary-General Ban Ki-moon called her "an anchor for our age," noting that her reign spanned decades "from the challenges of the Cold War to the threat of global warming," from "the Beatles to Beckham" and from "the television to Twitter."

"You have become a leading symbol of grace, constancy and dignity," Ban said.

The queen's U.N. speech, which followed a trip to Canada with her husband, the Duke of Edinburgh, was in her capacity as head of state of 16 U.N. member states -- the United Kingdom, Antigua and Barbuda, Australia, the Bahamas, Barbados, Belize, Canada, Grenada, Jamaica, New Zealand, Papua New Guinea, Saint Kitts and Nevis, Saint Lucia, Saint Vincent and the Grenadines, the Solomon Islands and Tuvalu.

CNN's Gabriella Casanas, Katya Lebedev and Richard Roth contributed to this report