The testing is run by the state's health department and started with 3,000 samples this week based on a random selection of the state's 19 million people, New York Governor Andrew Cuomo was quoted by Xinhua news agency.
The testing is regarded as a key step to determine when and how to reopen the state's economy, while scientists voiced concern over its accuracy.
Dr. Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases, said there is still "way to go" to trust antibody testing in making the reopening decision.
"Unless that test has been validated and you can show there's a correlation between the antibody and protection, it is an assumption to say that this is something that we can work with," Fauci said on Monday's "Good Morning America" on ABC.
According to Cuomo, New York state recorded 478 COVID-19 deaths on Sunday, the lowest single-day death toll in weeks.
Though the state has passed the plateau, no one knows how long will it take to trek down the other side, said Cuomo.
"Think about what we've gone through. Think about how many New Yorkers we've lost and are still losing. We must tread very carefully," he warned.
The governor once again called on the federal government to provide funding to hard-hit states like New York, which needs hundreds of billions of U.S. dollars to fill its budget hole.
Cuomo said hospitals, schools and local government could face some 20 per cent budget cut unless Congress passes a 500-billion-dollar state aid bill in the coming days.
He said that if the federal government could fund businesses, it should not forget about "teachers and police officers and firefighters and transit workers and health care workers and nursing home staff" who are funded with the state budget.
Cuomo also called on Washington to provide hazard pay for essential public workers who are risking their lives on the front lines day in and day out and proposed a 50 per cent bonus for them.
"Essential public workers are the ones on the front lines every day carrying us through this crisis, and we must ensure their efforts and sacrifice are appropriately recognized," said the governor.
"This crisis is not over yet, and as long as these workers continue to work and expose themselves to the virus, they should be properly compensated," he added.
In New York City, Mayor Bill de Blasio said on Monday that permits for major events in the city, including the Pride March, will be cancelled through June. Summer events are expected to be held later this year.
"We will do it at the right time," de Blasio said. "We're not doing anything but what is right to protect New Yorkers and this country."
As of Monday evening, the state of New York has reported over 253,000 cases and more than 18,000 deaths. New York City alone recorded over 141,000 cases, according to a tally kept by Johns Hopkins University.
( With inputs from ANI )