PALM BEACH, Fla. — In a Tax Day groundswell of calls for President Trump to release his tax returns, hundreds of protesters marched to Mr. Trump’s Mar-a-Lago getaway on Saturday in Florida, and thousands more gathered in Washington and other cities across the country.

On a waterfront patch facing Mr. Trump’s resort, where he is spending the weekend, demonstrators chanted “Pay! Your! Taxes!” and held signs calling him “Chicken in Chief” — the chicken being a symbol at the rallies of how Mr. Trump was “scared” to follow decades of presidential practice in releasing the returns.

“This is the closest we have come to making sure he sees us and hears us,” said Debbie Wehking, 66, a school principal from Miami. “He needs to show us his tax returns so that we can tell who’s influencing his decisions, who he owes money to, who he’s doing business with — really so we can figure out whether he needs to be impeached.”

Mr. Trump avoided the protest, taking a more circuitous route in his motorcade as he returned from a morning outing to his golf club in West Palm Beach. But while the president was spared the sight of chanting, sign-waving crowds, the demonstrations were heard around the country, in some cases snaking past properties bearing the Trump name.