WASHINGTON — Tens of thousands of demonstrators staged a boisterous fourth Women’s March here on Saturday, a noisy, frigid, drizzly rally where demands for equal rights competed with an inescapable subtext: President Trump had to go.

The march, a reboot of sorts for an event that has been dogged by internal strife, was intended to highlight climate change, reproductive rights and immigration, three issues chosen by supporters and organizers. But many of the placards hoisted amid the throng mocked or assailed Mr. Trump, demanded his impeachment or urged his defeat in November.

“It’s all about Donald Trump,” said Laurie Kaczanowska, 66, a retired criminal prosecutor who came from Doylestown, Pa., with friends to make the trek from a downtown plaza past the White House and back. “This march is about the many issues that face women and families, so climate change, of course, is up front. But here and now we have to pay attention to protecting our republic’s democracy. Because I think that’s in danger.”

In some ways, the focus on the president was a return to the driving factor of the first march, held the day after Mr. Trump’s inauguration in 2017. And many marchers said the administration’s policies could not be separated from the issues they were protesting.