JERSEY CITY — With Wall Street offices, brownstone-lined streets, star chefs, and even Citi Bike, New Jersey’s second largest city often resembles a more affordable, if less glamorous, mini-Manhattan — a sentiment a growing number of tourists now share, as they look here for cheaper accommodations.

Yet Jersey City could soon have something New York does not. On Monday, Mayor Steven M. Fulop will introduce legislation to legalize the use of all short-term sleepover web services, like Airbnb and HomeAway. The law is expected to be approved by November.

In exchange for agreeing to let some of Jersey City’s 262,000 residents rent out a couch, a bedroom or even their entire apartment or house on Airbnb, the company would charge users the same 6 percent hospitality tax currently levied on guests at the city’s dozen hotels.

Mr. Fulop anticipates the tax would generate between $600,000 and $1 million annually on the more than 300 Airbnb listings in the city. That would be added to the roughly $6 million the city makes on its hotel rooms each year.