WASHINGTON — Democrats hoped to put their wrenching intraparty debate over anti-Semitism to rest when they passed a catchall antibigotry resolution in the House this month, but Senate Republicans, eager to court American Jews outraged by the rise of anti-Semitism, have other plans.

Mitch McConnell, the Republican leader in the Senate, is backing two new bills timed to be trumpeted at this week’s annual meeting in Washington of the largest pro-Israel advocacy group, the American Israel Public Affairs Committee. Mr. McConnell has already passed a measure this year giving local and state governments the authority to break ties with companies that boycott or divest from Israel.

The actions are part of a larger political strategy aimed, in part, at showing that Republicans are more willing to directly tackle anti-Semitic hate speech and anti-Israel language than divided Democrats in the lower chamber, Republican aides and operatives said. But hate speech has hardly been a longtime cause célèbre for the Republican Party, whose members have opposed efforts to expand similar protections to victims of discrimination based on gender and sexual orientation.

One measure, a “sense of the Senate” resolution, is intended as a direct rebuke of comments made by Representative Ilhan Omar, Democrat of Minnesota, who suggested that some American Jews had dual loyalties to both Israel and the United States. The bill, sponsored by Senator Ted Cruz, Republican of Texas, could reach the floor as early as this week, leadership aides said, and is likely to be passed unanimously or with only minimal opposition.