The former England captain asked leaders to put children at the heart of the Sustainable Development Goals, the new 15-year agenda that the UN General Assembly will adopt over the weekend.
Many of the goals concern children directly: ensuring access for all to quality education, eliminating poverty, providing food security, improving nutrition and promoting durable agriculture.
Beckham, who has been a UNICEF ambassador for 11 years, told the event attended by UN chief Ban Ki-moon that 2014 was "one of the most devastating years on record for children."
More than 15 million children were exposed to "extreme violence and many more affected by natural disasters," he said warning that "2015 is proving to be just as bad."
"As a UN ambassador and as a father it breaks my heart to see children continue to suffer," said the 40-year-old former mid-fielder for Manchester United, Real Madrid and LA Galaxy.
"Children all share the same hope for a better future. With the world focused on the new global goals there is a real opportunity to make that hope a reality," he said.
Ban and Beckham helped unveil a digital installation in the lobby of UN headquarters that delivers messages from children across the globe about their lives and hopes for the future.
"Every child has a voice but too often they are just not heard," said Beckham. "At this crucial time when all the world leaders are gathered here in New York... their voices will be heard."
Beckham said he would "personally not rest" until children, especially the most disadvantaged, are put "at the heart of the new global goals."
It was Beckham's second visit to New York in days. He was last in the Big Apple on September 13 to attend wife Victoria's fashion show and the men's final at the US Open.