WASHINGTON — The number of chronically homeless people and homeless veterans has dropped significantly in recent years, but the Obama administration still faces challenges in its effort to completely eradicate homelessness by 2020.

Those findings and others, based on a single-day snapshot of data taken in January, were contained in an annual report on homelessness released Monday by the Department of Housing and Urban Development.

Homelessness overall has dropped 5.7 percent since 2007, but the decline was just 0.4 percent since January 2011.

Shaun Donovan, the Housing and Urban Development secretary, said the continuing downward trend “represents a real accomplishment when you consider this country is still recovering from the worst economic downturn since the Great Depression.”

There were 633,782 homeless in the United States on the night in late January when more than 3,000 cities and counties took their annual count of sheltered and unsheltered homeless. Nearly half were located in just five states: California, New York, Florida, Texas and Georgia.

The data showed slight growth in rural and suburban homelessness — believed to be caused by the recession’s impact on families — but the problem remains highly concentrated in urban areas.

The largest improvement has come among veterans and the chronically homeless, populations that were the first targets of an Obama administration initiative, organized by the United States Interagency Council on Homelessness, which aims to end chronic and veteran homelessness by 2015, and all homelessness by 2020.

The number of homeless veterans dropped 7.2 percent since 2011 and 17 percent since 2009. The number of chronically homeless has declined 6.8 percent since 2011 and 19.3 percent since 2007. But there are still 62,619 homeless veterans and 99,894 chronically homeless people. A person is considered chronically homeless if they have been homeless for one year or more, or if they are disabled and have experienced at least four instances of homelessness in the past three years.

Eric Shinseki, the secretary of Veterans Affairs, said the government has been “building momentum,” and remains on track to meet the 2015 target date. His agency will devote $300 million in 2013 to a grant program that provides veterans and their families with support services, like help with utility bills or moving expenses, while they live in or transition to permanent housing. The investment represents a significant increase from the $100 million that was spent on the program in 2012.

“We’ve learned that these grants are one of our most effective tools: quick, agile, precise, timely and decisive in stopping downward slides for veterans and families,” Shinseki said, adding that he expects the funds to help serve about 70,000 veterans and family members.