By Agence France-Presse
The demonstrations were timed to coincide with the traditional April 15 deadline for annual tax filings, a massive date on the calendar for US households, and resulted in dozens of arrests.
For decades, US presidents and presidential candidates have released their returns voluntarily, although there is no legal obligation to do so. US law requires only the publication of a financial statement that estimates assets, including debt and revenue, but does not give details on the amount of taxes paid.
Trump, a billionaire property tycoon, released a financial statement but has kept his tax returns private, both during the election campaign and since taking office in January.
Protesters and political rivals have said he should make a fuller disclosure to remove any inkling of potential conflicts of interest between his business interests and his political decisions.
"Until he does, we'll never know what he's hiding or who his policies are designed to benefit," said organizers of the "Tax March" demonstrations on its website.
"We need a president who works for all Americans -- and a tax system that does, too," it added.
At least 21 demonstrators were arrested after Trump opponents and supporters clashed at a march in Berkeley, California, US media said.
Real men pay their taxes
In Washington, several thousand protesters of all ages gathered in front of the Capitol building housing Congress, holding signs such as "What is he hiding?" and "Real men pay their taxes."
A huge inflatable chicken with an orange-gold beak and a swirl of hair resembling Trump's mane was displayed on the sidelines of the Washington protest, and at other venues.
It was seen by some as the unofficial mascot for the protest -- to suggest that the Republican president was afraid, or chicken, to publish his records.
"If he's got nothing to hide, he should release his tax returns," said protester Liz Turner, 31.
Asked what she suspected was in them, Turner replied: "Maybe something to do with Russia?"
Ellen Lodwick, 67, a retired corporate researcher from Maryland who has participated in anti-Trump demonstrations since his November 8 election, cast doubt on the president's businesses.
"There are probably many illegal or questionable investments in things that could affect how he looks at government and legislation, because he's too connected," she said.
The protesters then marched along Pennsylvania Avenue towards the White House, shouting "shame" as they passed by the Trump International Hotel.
Trump again at Mar-a-Lago
In New York, thousands also marched, and demonstrations were held from Boston and Philadelphia on the East Coast to Seattle, San Francisco and Los Angeles out West, and cities and towns in between.
The Berkeley protests saw hundreds gather at a park, including Trump supporters who held a free speech rally, while opponents of the president's policies shouted and chanted. Several fights broke out, according to the East Bay Times newspaper.
Activists waved signs reading: "No! Pussy-Grabbing! No! Patriarchy! No! Fascist USA! Drive out Trump-Pence regime!" and "Fascist scum your time is done."
Trump has justified his refusal to publish tax returns by noting they are being audited. Federal tax authorities say that does not bar him from releasing the documents. Trump has repeatedly said he has used legal loopholes to minimize his tax burden.
"Disclosing tax returns is the very lowest ethical bar for a president, and we are going to insist that he clear it," Senator Ron Wyden, an Oregon Democrat, told the Washington crowd.
Trump was not in the capital during the demonstration; he is again spending the weekend at his Mar-a-Lago estate in Palm Beach, Florida, where several hundred "Tax March" protesters demonstrated outside Saturday.
"Pay your taxes!" several shouted One young girl held a small sign that read "Trump is a tax e-VADER" and showed an image of Darth Vader wearing a blond hairpiece.