MIAMI — Text messages portraying the campaign of Florida’s Democratic candidate for governor as anti-Semitic buzzed into the cellphones of some Jewish voters on Thursday night, escalating political attacks in a closely watched race that has already been ugly.

“Newly unearthed comments made by Florida Democratic gubernatorial candidate Andrew Gillum’s running mate raise serious concerns about Gillum’s ever-mounting ties to blatant anti-Semitism,” the text messages read.

The messages referred to comments made nearly two decades ago by Chris King, Mr. Gillum’s pick to be lieutenant governor, when Mr. King was in college.

Mr. Gillum’s campaign called the messages a sign of “abusive tactics” by his Republican opponent, former Representative Ron DeSantis.