Michael Bloomberg's decision to break up Occupy Wall Street's protest in Zuccotti Park has pitched the New York mayor into a battle that goes to the heart of the US's fiercely protected right to freedom of speech.

Bloomberg set out his case on the legal issues in his first speech after the police moved in early on Tuesday to clear out protesters.

"From the beginning, I have said that the city had two principal goals: guaranteeing public health and safety, and guaranteeing the protesters' first amendment rights. But when those two goals clash, the health and safety of the public and our first responders must be the priority," he said.

Early on Tuesday, lawyers for Occupy protesters managed to get a court order ruling that the protesters could return to the park after the clearance. The order from New York supreme court judge Lucy Billings allows protesters to bring tents and other equipment back into the privately-owned park, and also barred police from making further evictions or for arresting anyone unless they were breaking the law.

Despite the ruling, hundreds of New York police blocked protesters from returning to the park, and more arrests were made as the two sides headed back to court for a second hearing.

Constitutional lawyers said health and safety was unlikely to trump the first amendment. Darius Charney, attorney with the Center for Constitutional Rights (CCR), said the right of people to assemble peacefully in political protest was one of the most fundamental rights under the first amendment.

"In my view, the health and safety issues are rather minimal in comparison to the first amendment issue," he said.

All speech is protected under US law, but political speech has the greatest legal protection.

"This is a very classic example of the right of people to assemble in peaceful protest to air their very serious concerns about the direction this country is heading in. It's very much a political act," Charney said.

There are factors that can over turn the right to protest: violent conduct, for example, incitements to violence or civil disobedience.

Bloomberg's decision to invoke health and safety seems to be an admission that those arguments were unlikely to hold up.

Charney said health and safety arguments looked weak too. "Protesters were not blocking traffic, there were no accusations of crimes, noise was being kept to a minimum in the evenings. I think the balance of the argument is against health and safety."

The Occupy protests are an example off what the law calls "expressive protest" – protests that are expressed through physical action, the most famous, and controversial, example being the burning of the US flag or the Qu'ran.

"Occupying the centre of Wall Street, in protest against the damage some believe those who work there have done to this country, could not be a clearer example of expressive protest," said Michael Ratner, CCR's president.

If Bloomberg fails to get the protesters legally evicted on health and safety grounds, he may have to fall back on the park rules to make life difficult for protesters. But here, too, he faces difficulties.

Zuccotti Park is a public-private park owned by Brookfield Properties and was built in return for it to be open to the public 24 hours a day.

Before the protests started, the park's rules did not specify that people could not occupy the park 24 hours a day or sleep there. City officials are likely to let protesters back in to the park but will probably move to ban tents, tarps or camps, a move that will leave protesters facing another obstacle to freedom of speech – New York's bitter winter.