Michael R. Bloomberg, who has committed nearly $1 billion to aid anti-tobacco efforts, is now stepping into the campaign to combat vaping, announcing a $160 million push to ban flavored e-cigarettes.

Mr. Bloomberg, the former mayor of New York City, said that his Bloomberg Philanthropies would aim to ban the flavored e-cigarettes in at least 20 cities and states.

His announcement on Tuesday was among a series of developments meant to heighten pressure and scrutiny on the vaping industry, amid a sudden and largely unexplained public health scare that has linked vaping to six deaths and hundreds of illnesses.

In New York, Gov. Andrew M. Cuomo vowed on Monday to introduce a bill to ban the sale of e-flavored cigarettes, and directed the state Department of Health to subpoena companies that market or sell so-called thickening agents, which are sometimes added to black market vaping products. A state laboratory, which detected the agents in vaping products collected from New York’s patients, found that they were nearly pure vitamin E acetate oil, which officials have said is a potential cause of the illnesses.