"We're serious about enforcing quarantine", Cuomo tweeted.
The state's COVID-19 hospitalizations dropped to 799, the lowest since March 18.
The latest order supports increased contact tracing, which is the process of mapping or cataloging the recent interactions had by someone who's tested positive for a virus. It will be enforced downstate by the Port Authority.
Any violation of a quarantine or isolation order issued to an individual pursuant to the Commissioner of the Department of Health's travel advisory by a local department of health or state department of health may be enforced pursuant to article 21 of the public health law, and non-compliance may additionally be deemed a violation pursuant to section 12 of the public health law subject to a civil penalty of up to $10,000.
Overall the state has recorded 24,974 deaths related to the coronavirus.More news: $114000 Bid for Super Mario Bros
"Fool me once", Cuomo said.
Even as he gave New Yorkers hope that students can return to classrooms soon, Cuomo attacked President Donald Trump for mismanaging the virus.
"Everyone wants to reopen the schools", he said during his briefing.
Schools can only reopen if their region is in Phase Four of the state's reopening plan0, and the daily infection rate remains 5% or lower over a 14-day average through August. "We're not going to put our children in a place where they're in danger".
The positive testing rate remained low in NY at 1.04% and about 1.3% in. But Gov. Andrew Cuomo urged people to remain vigilant with mask wearing and social distancing.More news: Aussie COVID-19 vaccine begins human trials
Cuomo continued to call for caution, noting the rising number of cases in other states.
Enforcement teams in Syracuse and other Upstate New York cities will include state Department of Health peace officers and staff supported by New York State Police personnel, according to Cuomo's office.
Travelers who do not comply could face a $2,000 fine and a hearing for a court-ordered quarantine.More news: Betsy DeVos vows students will return to classes this fall