Under the threat of a federal contempt citation, the leader of a suburban New York county agreed Wednesday to sign the same fair-housing bill he vetoed in 2010 — if the county Legislature passes it again.

Westchester County Executive Robert Astorino sent the bill back to the Board of Legislators, urged its passage and said he would approve it.

“If the proposed legislation is adopted by the County Board, I will sign said legislation in accordance with my court-ordered obligations,” Astorino wrote.

The bill relates to the 2009 settlement of a desegregation lawsuit against Westchester. One of the terms of the settlement was that the county executive promote legislation against “source of income” discrimination — for example, when a landlord refuses a tenant because the tenant plans to use federal vouchers to pay the rent.

Federal officials have said such refusals often serve as covers for racial discrimination.

When Astorino vetoed the bill, he claimed the duty to promote it applied only to the previous county executive, who had agreed to the settlement. He also called it a federal intrusion on private property.

When he lost a long court battle, he asked the Legislature to re-introduce the bill. But the Department of Justice said Astorino had to go further. It demanded that he submit the legislation himself and agree in writing to sign it or face possible contempt-of-court charges.

Ned McCormack, a spokesman for Astorino, said Astorino believes he was already in compliance and “today’s letter goes even further to show unambiguously that we’re complying.”

Justice Department spokeswoman Ellen Davis said the department would have no comment.

It’s not clear that the bill will pass the Legislature and it’s not known how the federal government will react if it fails.

It’s also not known whether Astorino’s actions Wednesday affect another deadline, also related to the housing settlement.

The Department of Housing and Urban Development has demanded the county provide by Thursday an acceptable analysis of exclusionary zoning practices in Westchester.