The New York mayor, Michael Bloomberg, has accused the Occupy Wall Street protesters of trying to destroy jobs in the city.

In his weekly radio show, Bloomberg said the protests against the city's financial services were "not productive" given the importance of the sector to the local economy.

"What they're trying to do is take the jobs away from people working in this city," he said.

"If the jobs they are trying to get rid of in this city – the people that work in finance, which is a big part of our economy – go away, we're not going to have any money to pay our municipal employees or clean our parks or anything else."

But Bloomberg acknowledged he was sympathetic to some of the protesters' complaints.

"There are some people with legitimate complaints," he said.

The protesters are angry about the 2008 Wall Street bailout that they say allowed banks to reap huge profits while average Americans suffered high unemployment and job insecurity.

Wall Street is the backbone of the New York state economy, accounting for 13% of tax contributions.

The protesters have been camped out in Zuccotti Park in Manhattan since last month, staging mainly peaceful demonstrations and marches, although there have been some clashes with the police.

On Wednesday, about 5,000 people marched on New York's financial district, the biggest rally so far. Dozens of people were arrested and police used pepper spray on some protesters.

The demonstrators are also campaigning against other social and economic inequalities in American life, including the gap between rich and poor, as well as what they regard as a corrupt political system.

The protest movement has now spread to other US cities from Tampa to Seattle, leading senior politicians to cautiously express sympathy with some of their concerns.

On Thursday the president, Barack Obama, and the vice-president, Joe Biden, acknowledged the frustration and anger of the protesters.

The New York governor, Andrew Cuomo, has also said he understands the anger being felt by the protesters but had to balance that with the economic importance of Wall Street to the state.