The call for action comes as UNICEF released a report Tuesday morning that showed lagging progress on the issue.
The report says the world is making insufficient progress on meeting the fourth UN Millennium Development Goal — to reduce the child mortality rate as of 2015 by two-thirds from the 1990 level.
The report says that at the current rate, that goal will only be met in 2026.
Harper has made maternal, newborn and child health his signature foreign aid priority, recently pledging another $3.5 billion over five years to 2020.
Harper will address the assembly in the coming week and take part in a separate event on the issue with Secretary General Ban Ki-moon on Sept. 25.
"With the prime minister's emphasis on maternal, newborn child health, this is a chance to stand up before the UN and say, 'this is Canadian leadership; we're going to put our money where our mouth is, and we think that others should as well'," UNICEF Canada President David Morley said in an interview.
"If we don't step up, we won't be able to save all these lives. Targets that we thought we'd meet now, we're not going to meet until after 2025."
Morley echoed an overarching finding of the report: even though great progress has been made in improving the survival of children under age five, much more needs to be done.
"But despite these advances, the toll of under-five deaths over the past two decades is staggering: between 1990 and 2013, 223 million children worldwide died before their fifth birthday," the report says.
Although progress has been made, pneumonia, diarrhea or malaria "are still the main killers of children," which last year accounted for one-third of deaths among children under the age of five, it says.
Change is possible, however.
"The world has the knowledge and solutions to save ever more women, newborns and children dying from causes that are easily avoidable," the UNICEF report says.
Harper announced his focus on the health of kids and moms in poor countries when he made it his signature initiative of the 2010 G8 leaders' summit that he hosted in Ontario.
He originally committed $2.8 billion over five years to the Muskoka Initiative.
Ban appeared at an international conference that Harper hosted in Toronto last spring and gave a ringing endorsement to the initiative before Harper pledged billions more.
The secretary general is spearheading his own international effort help mothers, newborns and young children.