As a 2-year-old tobacco class action trial grinds toward a conclusion in Miami, a federal judge in Brooklyn is quietly pushing to trial a series of potentially multibillion-dollar tobacco cases, starting in June-at a clip of one trial a month.

Industry lawyers are scrambling to derail or slow down the litigation train. They say that the cases before U.S. District Judge Jack B. Weinstein are legally indistinguishable from suits that have been thrown out of federal courts across the country.