Protesters against US President Donald Trump and his policies braved frigid temperatures in parts of America on Monday, shouting “No kings on Presidents Day” in East Coast cities and attempting to enter the Arizona Statehouse to oppose a bill that would bolster fast-changing federal immigration enforcement.

In Florida and California, local media outlets reported on hundreds of protesters carrying out “Not my Presidents Day” protests.

The “No Kings" theme was orchestrated by the 50501 Movement, and marked the second set of protests criss-crossing the nation in less than two weeks.

A similar nationwide event on February 5 drew participants in dozens of cities.

Both sets of rallies denounced Trump and billionaire adviser Elon Musk, the leader of Trump’s new Department of Government Efficiency, an outside-government organisation designed to slash federal spending.

Nearly 1,000 people marched in the snow from the Statehouse in Boston to City Hall, chanting “Elon Musk has got to go” and other slogans.

The temperature was below freezing.

Boston protesters, some dressed in Revolutionary War-style clothing, carried signs saying such things as “This is a Coup” and “Cowards Bow to Trump, Patriots Stand Up.” One sign had a depiction of Uncle Sam saying “I Want You to Resist.”

“I thought it was important to be here on Presidents Day to demonstrate for what America stands for,” said Emily Manning, 55, a Boston engineer who came to the rally with her two teenage sons.

“American values are not the values of the plutocracy or the limited few rich people.”

Organisers of Monday’s protests, which were focused on state capitals and major cities including Washington, DC; Orlando, Florida; and Seattle, said they were targeting “anti-democratic and illegal actions of the Trump administration and its plutocratic allies.”

One sign at the rally that attracted hundreds in the nation's capital said, “Deport Musk Dethrone Trump.”

The rallies followed a series of Trump executive orders and came just days after layoffs across federal agencies as part of an effort to reduce the government workforce. (AP)