“Our campaign is going to end the grotesque level of income and wealth inequality which exists in America today,” said Mr. Sanders, who was joined by Representative Alexandria Ocasio-Cortez, a standard-bearer of the progressive left. “So tonight we say to Michael Bloomberg and other billionaires: Sorry, you ain’t going to buy this election.”

He also derided Mr. Bloomberg’s intended strategy of bypassing the key early voting states where so many of the current candidates are devoting time, money and resources.

“You’re not going to get elected president by avoiding Iowa, by avoiding New Hampshire, South Carolina and Nevada,” Mr. Sanders said. “You’re not going to buy this election by spending hundreds of millions of dollars on media in California. Those days are gone.”