A bill that would create a list of foreign tax havens, and give the U.S. Treasury Department new tools to impose sanctions on them, has set off an intensive lobbying push by locales that don’t want to be named in the legislation.

To battle the Stop Tax Haven Abuse Act, Malta, the Isle of Man, the Cayman Islands Financial Services Association and others have spent more than $800,000 on lobbyists at firms including Covington & Burling; Son­nenschein Nath & Rosenthal; White & Case; and Quinn Gillespie & Associates.