WASHINGTON — The Trump administration moved on Thursday to eliminate an Obama-era program intended to combat racial segregation in suburban housing, saying it amounted to federal overreach into local communities.

The rule, introduced in 2015, requires cities and towns to identify patterns of discrimination, implement corrective plans and report results. The administration’s decision to complete a process of rescinding it culminates a yearslong campaign to gut the rule by conservative critics and members of the administration who claimed it overburdened communities with complicated regulations.

A new rule, which removes the Obama administration’s requirements for localities, will become effective 30 days after it is published in the Federal Register.

The move comes as President Trump’s re-election campaign contends with waning support among white suburban voters, particularly suburban women. The decision to eliminate the rule echoes the president’s recent efforts to appeal to white grievances as he seeks to maintain support in suburbs.

Within hours of the announcement by Ben Carson, the secretary of housing and urban development, Mr. Trump promoted his position on Twitter, posting a New York Post opinion article attacking the Obama housing rule and former Vice President Joseph R. Biden Jr., the presumptive Democratic presidential nominee, for supporting it.

“The Suburban Housewives of America must read this article,” Mr. Trump said. “Biden will destroy your neighborhood and your American Dream. I will preserve it, and make it even better!”

Mr. Trump had signaled last month that he was considering a full rollback of the rule. In a tweet, he wrote that the program had a “devastating impact on these once thriving Suburban areas.” He added, “Corrupt Joe Biden wants to make them MUCH WORSE.”

A spokesman for the Biden campaign called the elimination of the rule a distraction from the president’s handling of the coronavirus. Mr. Biden has proposed a housing policy that some Republicans say would undercut traditional suburban neighborhoods of single-family homes.

The Obama administration introduced its rule in 2015 to enforce the 1968 Fair Housing Act, which prohibits discrimination among housing providers. Failure to comply with the new rule jeopardized federal funds, and opponents claimed that it intruded upon the right of localities to make decisions about their own neighborhoods.

Dr. Carson has been a vocal opponent of the rule since his 2016 presidential bid. After he became housing secretary, the former neurosurgeon announced plans to suspend the program in January 2018, citing concerns raised by cities that struggled to comply with its requirements. He claimed that he would delay its resumption until communities had the necessary tools.

Two years later, the department published a proposal that would water down the original rule by eliminating the original mandate that cities and towns address housing discrimination.

A study from researchers at the Massachusetts Institute of Technology found that under the Obama rule, municipalities proposed more ambitious fair housing goals. Justin Steil, a co-author of the study, said that the program initially faced some difficulties, including complaints from localities that its requirements were onerous, but that those issues could have been resolved with time.

The elimination of the Obama-era rule is one of several efforts by the housing department to roll back housing regulations. It announced in August a proposal that would make it more difficult to prove some discrimination cases — those known as disparate impact claims — under the Fair Housing Act by establishing a higher bar of proof.

The new and final replacement for the Obama-era program, called Preserving Community and Neighborhood Choice, broadly reinterpreted the meaning of “affirmatively furthering fair housing.” Now, it makes no mention of segregation.

The housing department and the Office of Management and Budget waived the comment period for the new rule to speed its enactment, which raised concern among critics of the administration’s decision.

They argued that the old rule’s elimination had killed the first effort in decades to ensure the protections afforded by the Fair Housing Act. Diane Yentel, president of the National Low Income Housing Coalition, said the Trump administration was exploiting the political ramifications of a racially motivated policy change to boost his re-election campaign.

Shaun Donovan, the former housing secretary who created the Obama administration policy, was scathing in his criticism of the Trump administration’s move.

“This is a blatantly racist appeal to and attempt to return us to an era when the federal government actively implemented racist policies based on the false notion that Black families moving to white communities brings down property values,” said Mr. Donovan, who is now running for mayor of New York City.

The move to end the program also comes amid monthslong protests against racism spurred by the death of George Floyd. The disparity in homeownership between Black and white households is the highest it has been in 50 years.

This new rule “will take us backwards,” said Debby Goldberg, a vice president at the National Fair Housing Alliance. “If you’re looking to tackle the problem of segregation and widespread systemic discrimination — if you’re looking to create a prosperous country where that prosperity is shared by everybody — then adopting this rule is 100 percent the wrong move to make.”

But in his announcement on Thursday, Dr. Carson called the old rule “a ruse for social engineering under the guise of desegregation.”