WASHINGTON — The March for Truth, the latest in what has become nearly weekly demonstrations of various stripes against the Trump administration, drew a sign-waving crowd to the Washington Monument on Saturday to protest possible collusion between associates of President Trump and Russian officials in the 2016 election.

As new revelations have continued to emerge five months into the administration — the latest involving reported efforts by Jared Kushner, Mr. Trump’s son-in-law and adviser, to create a secret back channel to Russia — the protest was organized on Twitter under the banner #MarchforTruth.

The several dozen demonstrators in Washington said they were demanding a well-staffed, independent commission, removed from the White House’s influence, to investigate the possibility of collusion. They also called for Mr. Trump to release his tax returns, saying the documents could shed light on any connections to Russia.

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While the Justice Department has appointed a special counsel, the former F.B.I. director Robert S. Mueller III, to oversee the bureau’s Russia investigation, Mr. Mueller is not fully independent because he could be fired at the president’s direction.

One of the speakers who addressed the crowd, Terry O’Neill, the president of the National Organization for Women, said, “If, in fact, a hostile, foreign government has installed a puppet as president of the United States, that affects the entire mission of my organization to elect good, progressive, feminist candidates to office.”

Mr. Trump has dismissed suggestions that his election victory was aided by the Russians, calling such allegations “fake news.”

Some celebrities, such as the actors Debra Messing, Alyssa Milano and Javier Muñoz, gave money or other support to the march, and related events were held in other cities. Many of the protesters used the opportunity to try to draw attention to a longer list of grievances with the administration, holding signs about issues that had been the subject of previous demonstrations, like climate change, women’s rights, a proposed tax overhaul and science.

Sharon Soler, of Silver Spring, Md., who had brought her 10-year-old daughter, Sophia, said: “This is her future. This is her country. She needs to stand up for her rights. I want these institutions to be around when she’s older.”

Eric Pavlat, of College Park, Md., held a sign that read “Weekly Churchgoer Against Trump.” He said that in the past, he had mostly attended marches opposing abortion rights.

“I want other people to know that not only Democrats and seculars want the truth from the president and his administration,” he said, “that there is momentum on their side — and they are winning at convincing and persuading other people who weren’t just Clinton voters in the first place.”

An NBC News/Wall Street Journal poll that was conducted days before Mr. Mueller’s appointment on May 17 found that more than three-fourths of Americans believed that an independent commission or special prosecutor should take over the Russia inquiry.

Rena Verdi, of Columbia, Md., said she was attending her third march. “The Women’s March in January started it all,” she said. “But nothing has gotten any better. As a matter of fact, things have gotten worse. All of these ties to Russia are really problematic, and we need to get to the bottom of it.”

An hour before the March for Truth was scheduled to begin, dozens of Trump supporters gathered in Lafayette Square, just north of the White House, to celebrate Mr. Trump’s decision to withdraw from the Paris climate accord.

The Pittsburgh Not Paris rally, a name inspired by Mr. Trump’s comments in the Rose Garden on Thursday in which he said that he had been elected to serve American interests first, was organized by Virginia Republicans. The event seemed to have drawn as many journalists as demonstrators.

Across the park, in yet another gathering, about 30 children formed a chorus to sing Michael Jackson’s “Man in the Mirror” and the U.S.A. for Africa song “We Are the World” while tourists and other spectators looked on.