Mr Cuomo said Saturday's incident was the 13th anti-Semitic attack in NY since December 8.
He pleaded not guilty. Bail was set at $5 million.
Still covered in blood, Mr Thomas was reportedly arrested in his auto about 50km away, two hours after the attack.
Grafton Thomaswas driving a Nissan Sentra across the George Washington Bridge into New York City when his car's tag was captured by a license plate reader at about 11:45 p.m. Saturday, authorities said.
Authorities were yet to provide a motive.
Kohn told CNN he saw the suspect try to run into a nearby synagogue, but someone noticed and closed the doors before he was able to get in.
"I asked, 'Who is coming in, in the middle of the night, with an umbrella?'" said Kohn.
A witness, Josef Gluck, told the Associated Press that a man "came in wielding a big knife, sword, machete - I don't know what it was".
Hanukkah is an eight-day Jewish holiday marking the rededication of the second Jewish Temple in Jerusalem - the Holy Temple in the 2nd century B.C.
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Armed members of the Jewish community stand guard at a celebration, Sunday, Dec. 29, 2019, in Monsey, N.Y. As more Orthodox Jews have moved into the community, other residents taunted them anonymously online, then etched swastikas onto the dirty window of a van and a "for sale" sign in front of a home.
"We are outraged because the answer is clear: the Jewish community NEEDS greater protection", Greenblatt tweeted, demanding more protection for Jewish communities and consequences for the perpetrators of the attacks.
The attack on the seventh night of Hanukkah occurred amid a series of violent attacks targeting Jews in the region that have led to increased security, particularly around religious gatherings.
Six months before that, a gunman killed 11 worshipers at the Tree of Life synagogue in Pittsburgh in the deadliest anti-Semitic attack in us history.
Following Saturday night's attack, Cuomo also directed the state's Hate Crimes Task Force to investigate.
Monsey, near the New Jersey state line about 35 miles (56 kilometers) north of New York City, is one of several Hudson Valley communities that has seen an influx of Hasidic Jews in recent years. "That is not acceptable in New York City or anywhere in this country or anywhere in this world".
New York City's police department said on Friday its officers were stepping up patrols in heavily Jewish neighbourhoods in response.
Brown also said the phone showed searches for Jewish temples in Elizabeth, New Jersey and Staten Island, both on December 18, and for prominent American companies founded by Jews on December 27.
Wieder said anti-Semitism began to rise in the area about a decade ago and has increased noticeably in the past five years.
"We must all come together to fight, confront and eradicate the evil scourge of anti-Semitism", the president said.
Kim Thomas (left), mother of Grafton Thomas, the man accused of stabbing five people at a Hanukkah celebration, and attorney Michael Sussman (center) listen as the Rev. Wendy Paige speaks about Grafton Thomas at a news conference in Goshen, N.Y., on Monday.