WASHINGTON — A Republican group backed by the casino magnate Sheldon Adelson is starting a new effort in battleground states to win over Jewish voters who could be persuaded to turn away from President Obama and support Mitt Romney.

The group, the Republican Jewish Coalition, plans to begin a multimillion-dollar advertising campaign in the coming weeks called “My Buyer’s Remorse,” targeting voters in Florida, Ohio and Pennsylvania, aides said. The campaign uses testimonials from people who say they regret supporting Mr. Obama because of his economic policies and his posture toward Israel, in hopes of cutting into the wide advantage Democrats have held over Republicans among Jewish voters.

It is the latest foray into the election by Mr. Adelson, a staunch supporter of Israel who has vowed to spend as much as $100 million to defeat Mr. Obama. It marks an escalation of the partisan politics over Middle East policy and represents an emerging Republican strategy of highlighting voters who supported Mr. Obama four years ago but are now expressing disappointment, while signaling to others that they are not alone in shifting their allegiances.

Mr. Adelson and other members of the group’s board have pledged at least $6.5 million to build a comprehensive list of Jewish voters and to wage a word-of-mouth campaign, amplified through social media and television advertising.