Senator Bernie Sanders of Vermont kicked off his effort to win the April 19 New York Democratic presidential primary with a large, boisterous rally in the Bronx on Thursday night, highlighting his local roots and telling New Yorkers that he would work to make sure people have well-paying jobs, affordable housing and access to good public education.

Mr. Sanders spoke to thousands of supporters at St. Mary’s Park (the campaign said 18,500 turned out), where he vowed to provide more resources to the Bronx and other communities across the country. He also told supporters at the outdoor event that they would be critical to winning the nomination and to carrying out his policies.

“What this campaign is about is creating a political revolution,” Mr. Sanders told his cheering supporters. “You are the heart and soul of this revolution.”