Despite strides made in stamping out homelessness and building affordable homes in Connecticut, the high cost of housing continues to burden hundreds of thousands of households in the state, a new report says.

The Partnership for Strong Communities’ annual housing assessment, released Tuesday, found virtually no change in the number of Connecticut households devoting 30 percent or more of their income to housing, the definition of being “burdened” by housing costs. The percentage of renters so burdened fell to 49.1 percent from 49.7 percent in 2014, and to 30 percent of homeowners, down from 30.8 percent.

Among households considered “severely burdened” by housing costs, 26.4 percent of renters and 12.5 percent of homeowners were spending more than 50 percent of their income on housing.

Over the last year, Connecticut’s “housing wage” — the amount a worker must earn to afford a typical two-bedroom apartment — rose to $24.72 an hour, up from $23.02 two years earlier, according to the report. It’s the eighth-highest in the nation.

The nonprofit partnership referred to its report as “a tale of two realities,” citing achievements as well as trends that are cause for concern. It credited Gov. Dannel P. Malloy, state Housing Commissioner Evonne Klein, lawmakers and others with working to end homelessness among veterans and significantly reduce it among the chronically homeless.

In November, the state Department of Housing reported that it had produced 1,028 new housing units, including 929 that were considered affordable.

“The progress is undeniable,” Alicia Woodsby, the partnership’s executive director, said. “But so is the work we still must do.”

The report notes that rental housing costs have been rising because of high demand, a trend that’s likely to continue.

During the year, median gross rent climbed 3 percent to $1,108 a month, the 10th-highest among the states. The total number of renting households rose to 33.8 percent from 31 percent in 2008, while the number of home-owning households fell to 66.2 percent of all households, down from 69 percent in 2008.

“That fall-off in the demand for homeownership has kept grand lists and median home prices flat in recent years, with only modest increases in some regions,” the report says.

High rental costs are driven by demographics, said David Frink, a partnership consultant.

“For years, towns built single-family homes for baby boomers who now want to downsize,” he said. “And millennials coming out of school with college debt need somewhere they can afford to live.”

In New London, Marilyn Graham, executive director of Housing Opportunities for People, or HOPE Inc., said her organization, which rehabilitates blighted properties, believes strongly in home ownership. In pursuing grants, she relies in part on the Partnership For Strong Communities’ annual report, the latest of which she has yet to review.

“It’s hard to make a dent in the problem,” Graham said, referring to the lack of affordable housing. She acknowledged, however, that considerable progress has been made in eradicating homelessness.

HOPE was among three New London-based nonprofits awarded grants last week to assist their efforts at improving the city’s housing situation. Eversource provided $500,000 to HOPE and lesser amounts to Habitat for Humanity of Eastern Connecticut and the New London Homeless Hospitality Center.

The report found that in 138 of Connecticut’s 169 municipalities, less than 10 percent of the housing is affordable. In New London County, three municipalities are among the 31 in the state in which more than 10 percent of the housing is affordable: New London, with 23.5 percent; Groton, 22.7 percent; and Norwich, 19.2 percent.

Hartford, at 40.2 percent, has the highest percentage of affordable housing in the state.

b.hallenbeck@theday.com