The Syosset school district is conducting an investigation after swastikas, hate graffiti and the name of a notorious street gang were discovered over the weekend on school grounds, while Gov. Andrew M. Cuomo on Monday ordered State Police to assist in the probe.

Nassau police said the vandalism occurred between 2 a.m. and 4 a.m. Sunday on the walls, doors, and windows in the back of Syosset High School on South Woods Road, and included the phrase “MS13” — an apparent reference to the street gang. A police spokeswoman said the images were spray-painted in “various” colors.

In a statement Sunday, Syosset Superintendent Tom Rogers described the graffiti, which he said also were found at the adjacent South Woods Middle School, as “rude, crude and vulgar,” as well as “homophobic, misogynistic and anti-Semitic.”

He said the district would investigate “this incident doggedly, and we will deal with any future incidents aggressively.”

The district is “reviewing every aspect of our internal operations to prevent something like this from happening again.”

Cuomo said in a statement Monday that he was “appalled by the disgraceful anti-Semitic graffiti found at Syosset High School. No student should ever feel discriminated against or threatened because of their religion or ethnic origin. In New York, we have zero tolerance for bigotry and hate of any kind.”

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He directed State Police to work with the Nassau police department in its investigation.

In a Facebook post Sunday, school board member Josh Lafazan, who was visiting Tel Aviv, Israel, this week for a family wedding, called for increased security at district buildings.

Lafazan had planned to meet with community activists and civic leaders in Israel this week to discuss anti-Semitism on college campuses, given the presence of white supremacists and neo-Nazis in Charlottesville, Virginia, earlier this month.

“In the wake of Charlottesville, I thought a lot about hate in our country,” Lafazan said in a phone interview Monday. “Never could I have imagined such visceral hatred toward the Jewish people existed in my backyard.”

Lafazan is running as a Democrat for county legislator. His opponent, Legis. Donald MacKenzie (R-Oyster Bay), could not immediately be reached for comment. MacKenzie was among a group of local elected officials at a Monday news conference centered on denouncing the vandalism.

Officials in the school district also referenced the proliferation of hate-fueled speech and violence across the country in recent weeks.

“One need look no further than the nightly news to see that our nation’s broader commitment to tolerance is being tested,” Rogers said in his statement. “But I am convinced that Syosset’s dedication to diversity is not superficial.”

Rogers said that high school Principal Giovanni Durante greeted incoming students at Monday’s freshman orientation by reminding them that the community will not be “paralyzed by the acts of a few,” and the vandalism would not “dampen the excitement of a new school year.”