The Trump administration wants to shift the way it enforces an aspect of fair housing around the U.S., pivoting away from efforts to integrate lower-income housing into wealthier neighborhoods in favor of promoting more housing development overall.

The U.S. Department of Housing and Urban Development announced the change on Monday.

Mr. Carson said he wants to simplify the process for communities and address the proliferation of stricter land-use rules in recent decades. Home construction is near 60-year lows by some measures, in part because communities over time have layered on regulations that make development difficult and costly.

“I want to encourage the development of mixed-income multifamily dwellings all over the place,” Mr. Carson said. He hopes to have  a new rule in place by the fall.

The secretary pointed to Los Angeles as an example of how zoning rules stymie housing development. He said a large majority of the city’s parcels of land are eligible only for single-family home development, not larger projects that could house more people and help moderate price growth. “Of course you’re going to have skyrocketing prices that no one can afford,” he said.

Policy makers have long puzzled over how to create incentives for cities and towns to build more housing. Local officials are often in a difficult political position because the loudest voices among their constituents tend to be those objecting to development. At the same time, federal and state governments have limited control over local zoning.

Mr. Carson said the new rule would tie HUD grants, which many communities use to build roads, sewers, bridges and other infrastructure projects, to less restrictive zoning.

“I would incentivize people who really would like to get a nice juicy government grant” to take a look at their zoning codes, he said.

Advocate groups for housing for minorities and for those with low income have criticized the Trump administration for rolling back several Obama policies aimed at stepping up enforcement of the Fair Housing Act, which turned 50 in April. Critics say HUD has neglected its responsibility to enforce the act, contributing to inequities in homeownership, wealth and education for blacks and other minorities.

In the Obama era, officials prioritized making it easier for lower-income people to move to wealthier communities, citing research that showed it improved outcomes for children. HUD’s latest move is another sign that the Trump administration has a different philosophy.

Mr. Carson said he is unconcerned about what “theoreticians” will say.

“The last administration, when they put this together they really went down an ideological pathway,” he said. “We are going to look at the people who are actually affected, what are they saying, what will be helpful to them.”

Write to Laura Kusisto at laura.kusisto@wsj.com