The union which represents workers at those airports warned the strikes could resume at any time at those locations.
The cleaners work for PrimeFlight, which services planes for United Airlines, the largest carrier the airport.
Several hundred workers planned to walk off the job at NY area airports Wednesday but they suspended the planned strike after talks with American Airlines resumed.
"The company is telling them they'll be fired for organizing or the company will change the schedules of those involved in leadership", said Amity Paye, a spokeswoman for 32BJ SEIU, which is helping the group to form a union.
The workers walked off the job Tuesday night amid an ongoing dispute with employer PrimeFlight Inc.
The strike is also being held at several other airports and impacted operations in the East on Wednesday morning. The workers are alleging unfair labor practices.
A strike by workers at the four area airports is temporarily on hold, according to reports. Clint Smith, eastern vice president for Prospect Airport Services, which employs about 400 workers, had no comment, nor did Bill Stejskal, PrimeFlight's senior vice president for human resources. The strike would continue for at least three days.