ByLaura Kusisto, Wall St Journal

Airport contract workers rallied on Monday at Riverside Church; thousands are interested in joining SEIU. Kevin Hagen for The Wall Street Journal

A majority of 6,100 nonunionized workers at New York City’s three largest airports have turned in cards indicating interest in joining a union, according to a tally conducted Monday at a church on Manhattan’s Upper West Side.

The count, done by outside nonprofit groups, showed 4,051 workers had signed cards to join or are already members of 32BJ Service Employees International Union, union officials said. The union plans to seek signatures from more workers and hold demonstrations, building support for a formal vote to organize.

The union drive is directed at workers at La Guardia Airport, John F. Kennedy International Airport and Newark Liberty International Airport who are employed by contractors of the large airlines.

The workers are security guards, wheelchair attendants, baggage handlers and cleaners of bathrooms and aircraft.

If the workers join the union and successfully negotiate for higher wages, health benefits and paid vacation time, the costs could be passed along to airline passengers through higher ticket prices.

“I know it’s not going to be easy, but I am confident we will get a union,” Michael Carey, a Kennedy Airport security officer, said at a union rally in Riverside Church.