After years of pleading for higher wages, thousands of workers at the airports that serve New York City are on the verge of securing one of the highest minimum wages in the country.

The directors of the Port Authority of New York and New Jersey, which operates the airports, agreed on Thursday to consider raising the minimum wage for more than 40,000 airport workers to $19 an hour by the fall of 2023. That would amount to an increase of more than 80 percent in about five years for the lowest-paid workers at Newark Liberty International Airport, one of the three major airports operated by the Port Authority.

The possibility of a robust pay increase comes at a time of frustration that the wages of many American workers have not risen in line with the long expansion of the national economy.

The recommendation, which the agency’s board is expected to approve in June, could bring an end to years of rancor and dissension over pay at the airports. Representatives of the two states have been so divided on the issue that they created an uneven pay structure on the two sides of the Hudson River.