By Jonathan Allen

NEW YORK (Reuters) - The vandalism of more than a dozen headstones at a Jewish cemetery in Rochester is being investigated by a New York hate crime task force, the third known case of a Jewish cemetery desecration in the country in the last two weeks.

Democratic New York Governor Andrew Cuomo said he ordered the investigation at Waad Hakolel Cemetery given the wave of bomb threats that later proved hoaxes targeting Jewish community centers and vandalism at Jewish cemeteries in Philadelphia and St. Louis.

U.S. President Donald Trump, a Republican, has condemned the threats and attacks, although he has at times also questioned whether some perpetrators might be opponents of his seeking to link his new presidency with a rise in anti-Semitism.

Trump's election campaign last year drew support from some white nationalists and right-wing groups, despite his disavowals of them.

Besides the toppling of headstones at the Rochester cemetery, images of the deceased embedded on at least half a dozen headstones had been scratched away, although it was not clear how long ago, said Karen Elam, the director of community relations at the Jewish Federation of Greater Rochester.

"It's clear vandalism," she said in a telephone interview after touring the cemetery on Thursday afternoon to photograph the damage. "Any vandalism of a Jewish cemetery is de facto anti-Semitism."

Michael Phillips, president of the non-profit organization that oversees the cemetery, told the Rochester Democrat & Chronicle newspaper that there was no proof the vandalization was a case of anti-Semitism, citing the smaller scale of the damage in Rochester.

About 100 headstones were knocked over at a Jewish cemetery in Philadelphia last weekend, and about 170 headstones were knocked over in a Jewish cemetery in St. Louis.

Officials at the cemetery in Rochester did not return calls seeking comment. In 2014, vandals toppled more than 40 headstones at another Jewish cemetery near Rochester, but local police concluded the vandalism was not motivated by anti-Semitism, the Democrat & Chronicle reported.

(Reporting by Jonathan Allen; Editing by David Gregorio and Lisa Shumaker)