Twenty more of New Orleans’ homeless military veterans now have a place to call home.

Volunteers of America Greater New Orleans, the local arm of the national human services charity, on Wednesday unveiled its new Oscar J. Tolmas Veterans Center, a 20-bed shelter that will increase the capacity of the nonprofit’s transitional housing program for homeless veterans.

The program offers veterans temporary shelter and rehabilitation services, including substance abuse and mental health counseling, educational services, job training and placement, and permanent housing placement.

It’s part of the city’s goal to keep the local homeless veteran population at what President Barack Obama’s administration calls “functional zero” — meaning the city has a process and the resources available to immediately house a veteran who ends up on the street.

Obama and first lady Michelle Obama have urged cities across the country to all but eliminate veteran homelessness and have provided the cash to help, spending nearly $1.5 billion in 2014.

Mayor Mitch Landrieu took that goal a step further, asking local leaders to speed up the process by a year. And the city did so, housing all 193 veterans living on the streets in Orleans and Jefferson parishes by the end of 2014, according to the city, and earning national recognition.

Officials have since exceeded their initial goal, finding permanent housing for almost 400 veterans since that time, Landrieu said.

“There is no city in America that has done all the things that we are doing as quickly as we are doing it,” the mayor told a crowd gathered in the 3800 block of Pitt Street for a dedication ceremony.

Volunteers of America’s new center, named for a local World War II veteran, lawyer and horse-racing enthusiast who willed his assets to charity before his death in 2013, will help the nonprofit house up to 76 veterans.

The building was constructed in 1964 as an infant nursery and has served various purposes over the years, Volunteers of America President and CEO Jim LeBlanc said. It opened a few weeks ago and still has 10 beds available.

Separately, the city and the Downtown Development District will spend $2 million this year to build a low-barrier homeless shelter that will be available to all those who live on the streets, not just veterans. It will serve people who may be uncomfortable sleeping indoors but who still need care, City Councilwoman LaToya Cantrell has said.

It is scheduled to be completed by the end of 2016.

Follow Jessica Williams on Twitter, @jwilliamsNOLA.