Legions of demonstrators frustrated by international inaction on global warming descended on New York City on Sunday, marching through the heart of Manhattan with a message of alarm for world leaders set to gather this week at the United Nations for a summit meeting on climate change.

Coursing through Midtown, from Columbus Circle to Times Square and the Far West Side, the People’s Climate March was a spectacle even for a city known for doing things big, and it was joined, in solidarity, by demonstrations on Sunday across the globe, from Paris to Papua New Guinea.

“I’m here because I really feel that every major social movement in this country has come when people get together,” said Carol Sutton of Norwalk, Conn., the president of a teachers’ union. “It begins in the streets.”