New York landlords who overcharge tenants in rent-stabilized apartments would face sharply higher financial penalties under new legislation unveiled in Albany.

The bill was introduced Tuesday by Sen. Brad Hoylman and Assemblywoman Linda Rosenthal, both Democrats. It was prompted by ProPublica’s reports that up to 200,000 apartments that should be registered for rent stabilization in New York City aren’t, and that city and state officials have failed to police landlords who share in more than $1 billion in property tax breaks in return for limiting rents.

Rent-stabilized apartments afford tenants rights such as caps on annual rent increases and eviction protection. But decades of weak enforcement, lack of strong penalties and confusion have allowed many building owners to simply not bother registering with the state as the law requires.

The new bill would increase penalties for overcharging tenants to five times the overcharge for a first violation and 10 times the overcharge for a repeat offense, plus interest. Current law doesn’t discriminate between first-time and repeat offenders and limits penalties to three times the overcharge.

Even triple damages can add up to large penalties if tenants prevail in court. One tenant recently won an $877,000 refund from his landlord for overcharges in a rent-stabilized apartment on the Upper West Side. The apartment was subject to rent limits because the owner received a city tax break.

Hoylman said he hoped increased penalties would force more landlords to comply with the rent-stabilization laws. “Just the mere fact of heavier fines, I think, will give landlords pause,” he said.

Rosenthal also has a related bill, A2234, that would impose a fine of $2,000 per apartment for failing to register. Several New York City council members, also citing ProPublica’s reporting, have introduced legislation to impose a similar fine for not registering.

“It has to be painful; otherwise, it’s just chalked up as ‘cost of doing business,’ ” Rosenthal said.

The Rent Stabilization Association, which represents New York City property owners, declined to comment. Katie Goldstein, executive director of Tenants & Neighbors, the statewide tenants’ rights group, said she supports upping the overcharge penalty because “unscrupulous landlords are currently operating in an environment where they intentionally break the laws, and there are no consequences.”

Ellen Davidson, a tenant attorney with the Legal Aid Society, also welcomed the legislation but said that “with increased penalties needs to come increased enforcement.” Historically, city and state regulators have not aggressively enforced rent-stabilization laws, leaving tenants to fend for themselves.

The lax enforcement contributes to a huge gap in the number of apartments that should be stabilized but may not be. In November, ProPublica estimated that 50,000 apartments receiving property tax breaks under two programs — known as 421-a and J51 — had been left out of rent stabilization.

For more than two decades, New York City has estimated that there are about 1 million rent-stabilized apartments in the city. But state data indicate that, since 1994, the number of apartments actually registered has hovered between 804,000 and 870,000 — a difference of close to 200,000 units.

“This is an issue that I’ve been looking at for a while, hearing — largely anecdotally — that landlords were removing rent-stabilized apartments, in many cases willfully, off the books,” Hoylman said. “Now we have concrete evidence that not only it’s happening, but that it’s happening at a worrisome pace.”

With New York City Mayor Bill de Blasio aiming to add and preserve 200,000 units of affordable housing over the next 10 years, Rosenthal said the city should first make sure that every apartment that is supposed to be rent-stabilized is in compliance with the law.

“It’s not low-hanging fruit,” she said, “but it’s certainly hanging fruit.”