It's from a speech by Kofi Annan of Ghana, the (former) Secretary-General of the United Nations, delivered at the nuclear non-proliferation treaty review conference, United Nations, 2005. The very last lines of his speech read:
"The peoples of this world must unite, or they will perish...The atomic bomb has spelled [this] out for all men to understand."
Source: http://www.un.org/events/npt2005/statements/npt02sg.pdf
Is
peoples grammatically correct? Yes, and Kofi Annan used it quite effectively too, to describe all the people on this plant, all nations, as a single community. The following is from the
Usage Note at dictionary.com:
When peoples means “the entire body of persons who constitute a community or other group by virtue of a common culture, history, etc.,”... The aboriginal peoples of the Western Hemisphere speak many different languages.
Source: peoples - Definitions from Dictionary.com