The Federal Bureau of Investigation arrested a man in St Louis, Missouri on Friday suspected of making bomb threats to Jewish community centers and schools around the United States.

The Justice Department said Juan Thompson, 31, was thought to be behind at least eight of more than 100 threats made in recent weeks to Jewish schools, community centers and other institutions, that have stirred fears of a rise in anti-Semitism.

The agency said the threats were made as part of Thompson's efforts to harass an unnamed former girlfriend.

"Today, we have charged Juan Thompson with allegedly stalking a former romantic interest by, among other things, making bomb threats in her name to Jewish Community Centers and to the Anti-Defamation League," New York-based US Attorney Preet Bharara said in a statement.

"Threats of violence targeting people and places based on religion or race –- whatever the motivation –- are unacceptable, un-American and criminal."

Thompson allegedly emailed in threats against the Jewish institutions that indicated his ex-girlfriend was behind the threats.

He also made some in his own name, but as ploys to allege that she was trying to frame him for the crime.

Thompson was charged with one count of cyberstalking, which carries a maximum sentence of five years in prison.

Jewish cemeteries attacked

Officials said investigations remain open into the other threats against Jewish schools, community centers and other institutions, as well a vandalism against three Jewish cemeteries.

Many of the scores of bomb threats were phoned in. Jewish community officials say those calls appeared to use electronic devices to mask the voice and location of the caller or callers.

The Justice Department's Civil Rights Division, which investigates hate crimes, is leading the probe, officials said. But the statement on Thompson's arrest said his prosecution also involves the department's counterterrorism and general crimes units.

While the bomb threats appear to have halted in recent days, overnight Wednesday someone toppled about a dozen headstones and defaced pictures on them in a Jewish cemetery in Rochester, New York.

It was the third Jewish cemetery in two weeks to be vandalized. More than 200 headstones were overturned or broken in cemeteries in St Louis, Missouri and Philadelphia, Pennsylvania, adding to fears of a rise in open anti-Semitism in the country.

Meredith Dragon, chief executive of the Jewish Federation of Greater Rochester, said local police were not yet ready to determine whether what happened there was an act of petty vandalism or a targeted hate crime.

As no local Jewish community centers or schools were targeted in the recent spate of telephone threats, it "leads me to believe this has been local," she said.

Trump comments questioned

On Tuesday, President Donald Trump condemned the threats and vandalism in a speech before Congress, saying such acts "remind us that while we may be a nation divided on policies, we are a country that stands united in condemning hate and evil in all its forms."

But earlier Tuesday, according to Pennsylvania Attorney General Josh Shapiro, Trump suggested to a group of state prosecutors that some of the threats and acts of vandalism could be "the reverse," suggesting they were aimed not at Jews but at making others look bad politically.

Shapiro told NPR radio Thursday that such mixed messages from the president "stokes doubt" in the public about what is going on.

"I don't know what the president meant," he said. "But here's what I know, is that presidents must speak with moral clarity, not through mixed messages.... And this kind of wishy-washy speech leaves too much open to interpretation by the wrong people."