WASHINGTON — Thousands of scientists and their supporters, feeling increasingly threatened by the policies of President Trump, gathered Saturday in Washington under rainy skies for what they called the March for Science, abandoning a tradition of keeping the sciences out of politics and calling on the public to stand up for scientific enterprise.

As the marchers trekked shoulder-to-shoulder toward the Capitol, the street echoed with their calls: “Save the E.P.A.” and “Save the N.I.H.” as well as their chants celebrating science, “Who run the world? Nerds,” and “If you like beer, thank yeast and scientists!” Some carried signs that showed rising oceans and polar bears in peril and faces of famous scientists like Mae Jamison, Rosalind Franklin and Marie Curie, and others touted a checklist of the diseases Americans no longer get thanks to vaccines.

Although drizzle may have washed away the words on some signs, they aimed to deliver the message that science needs the public’s support.

“Science is a very human thing,” said Ashlea Morgan, a doctoral student in neurobiology at Columbia University. “The march is allowing the public to know that this is what science is, and it’s letting our legislators know that science is vitally important.”

The demonstration in Washington — which started with teach-ins and a rally that packed the National Mall — was echoed by protests in hundreds of cities across the United States and around the world, including marches in Europe and Asia.

The March for Science evolved from a social media campaign into an effort to get people onto the streets.

Its organizers were motivated by Mr. Trump, who as a presidential candidate disparaged climate change as a hoax and cast suspicions on the safety of vaccines.

Their resolve deepened, they said, when the president appointed cabinet members who seemed hostile to the sciences. He also proposed a budget with severe cuts for agencies like the National Institutes of Health — which would lose 18 percent of their funding in his blueprint — and the Environmental Protection Agency, which faces a 31 percent budget cut and the elimination of a quarter of the agency’s 15,000 employees.

While traveling by motorcade to Walter Reed National Military Medical Center on Saturday, Mr. Trump passed dozens of demonstrators from the march holding signs, including one that said, “Stop denying the earth is dying,” according to a pool report. Later, the White House released a statement from Mr. Trump for Earth Day that did not mention the March for Science by name, but appeared directed at its participants. Calling science critical to economic growth and environmental protection, he said, “My administration is committed to advancing scientific research that leads to a better understanding of our environment and of environmental risks.”

“As we do so, we should remember that rigorous science depends not on ideology, but on a spirit of honest inquiry and robust debate,” he added.