Thousands of demonstrators, baking in the heat and boiling mad against US immigration policy, marched across the country Saturday to protest the separation of families under President Donald Trump's hardline policy.

Dubbed "Families Belong Together," the demonstration in Washington began at Lafayette Square where crowds gathered directly across from the White House before a planned march toward the Capitol.

In New York, families, young people, children and the elderly - both recent arrivals and long-time citizens - all stood under a burning sun as part of a protest which a police officer said already numbered "a couple of thousand."

"Say it loud, say it clear, refugees are welcome here," they chanted, also declaring a welcome for Muslims.

A band of drummers whipped up the fervor of a crowd carrying signs including, "Our New York is Immigrant New York," and "No Cages, No Ban, No Wall."

"Abolish ICE," said another sign, reflecting growing calls by activists for abolition of the country's frontline immigration enforcement agency.

Starting in early May, in an attempt to staunch the flow of tens of thousands of migrants to the southern US border every month, Trump ordered the arrest of adults crossing the boundary illegally, including those seeking asylum.