Mr. Bloomberg and his strategists have used various tactics to stress the parts of his biography that help soften his image. His ads describe his middle-class upbringing in Boston and highlight his philanthropic giving, for instance.

He has also started talking more often about his plan to raise $5 trillion in new tax revenue from high earners and corporations. His message to voters as he campaigns across the country has been, in essence, that the government should raise taxes on people like him because they can afford it.

The surcharge on trading, meant to raise money for social programs like expanded health care coverage, has been roundly criticized by the sort of pro-business groups that Mr. Bloomberg had long been sympathetic to, like the U.S. Chamber of Commerce.

The group immediately criticized the proposal. A transaction tax “hits Main Street, not Wall Street,” said Tom Quaadman, a chamber executive. He added that it would “increase the cost of capital, decrease investment, harm businesses and hurt Americans who are saving and investing.”

Rachel Nagler, a Bloomberg campaign spokeswoman, argued that such a tax “is an effective and relatively painless way to raise more tax revenue from the wealthy,” citing its use in Britain and Hong Kong. A 2018 analysis by Congress’s Joint Committee on Taxation estimated that a tax similar to the one proposed by Mr. Bloomberg would raise $777 billion over 10 years.

Mr. Bloomberg’s plan embraces many of the regulatory changes made in the years after the financial crisis, even though he has often argued that rules aimed at reforming Wall Street are bad for the economy. In 2010, Mr. Bloomberg urged Democratic lawmakers not to get too tough on the finance industry, and he criticized the Volcker Rule, which is meant to reduce speculative trading by banks. He called the proposed restrictions “shortsighted,” with the potential to reduce middle-class jobs.

On Tuesday, Mr. Bloomberg said he would toughen the Volcker Rule — although his idea is more like a major rewrite. It would assume that banks were engaging in safe practices as long as they didn’t gain or lose too much on a deal. Rather than getting in traders’ heads about what constitutes a speculative trade, he proposes taxing big gains and losses, reasoning that volatile outcomes beyond a certain threshold must be the result of overly speculative activity.