New Yorkers with family members in the country illegally will be able to more easily apply for the city’s highly competitive affordable housing lotteries as part of broader rules changes announced by City Hall on Wednesday, which are meant to expand eligibility.

The new rules will allow applicants to provide proof they pay their rent on time instead of submitting for a formal credit check, which required prospective tenants to put down their Social Security or taxpayer identification numbers.

“For too long, families without access to credit have faced barriers to the affordable housing they need,” said Mayor Bill de Blasio in a statement. “By allowing New Yorkers to submit rental history instead of credit checks, we are creating a fairer system for all New Yorkers.”

Under the new rules, tenants can bypass the credit check requirement by providing evidence they paid a year’s worth of rent on-time.

Previously, they were required to provide a Social Security or taxpayer identification number for a background check. Anyone not eligible to receive Social Security — including illegal immigrants — can receive an ITIN and complete the check.

Officials defended the rule change by claiming that credit check requirements often adversely impact African American and Latino applicants, but acknowledged the change also would make it easier for undocumented immigrants to apply.

“These new changes are a step towards promoting greater racial equity in our housing market and greater access to affordable housing, regardless of immigration status,” said Bitta Mostofi, who runs the Mayor’s Office of Immigrant Affairs.

Despite that claim, city officials later said that tenants will still be required to provide proof of employment through tax returns, pay stubs or letters of employment — effectively keeping households without an authorized immigrant or citizen from getting a lease.

A top de Blasio critic on the City Council quickly slammed the idea.

“It’s just the latest idiotic idea to come out of this administration,” said Councilman Eric Ulrich (R-Queens). “The mayor is setting up people to fail and is doing a disservice to New Yorkers who desperately need affordable housing.”

Additionally, the city’s housing agencies are dropping the charges for a credit check to $20 to comply with the state’s new rent laws. And City Hall is loosening the rules on household size to allow more people to cram into smaller apartments.

“By addressing the challenges many low-income New Yorkers face in the rental application process, we are creating more options for those in need of an affordable home,” said Eric Enderlin, president of the city’s Housing Development Corp.