Mayor Vincent C. Gray said Wednesday he’d like to close down the shelter for homeless families located on the D.C. General Hospital campus — home to 8-year-old Relisha Rudd until she went missing more than a month ago — but he said that community concerns would make it difficult to open enough smaller facilities across the city to compensate for its loss.

“We need smaller places, but the problem we have is the NIMBYism that exists,” he said in a reference to not-in-my-backyard types. “People will say, ‘Yeah, that’s a great idea; just don’t put it in my neighborhood.’ We’ve got to have the support of the leadership in this city beyond just the government leadership, the elected leadership … to say, ‘Yes, we want to work with you,’ so families when they have a crisis, they will be able to go to a place that is different than D.C. General.”

Gray’s comments came a day after he convened a John A. Wilson Building meeting with major residential landlords as a part of his “500 Families, 100 Days” effort to house those now in shelter beds. On Tuesday, the Gray administration also issued a statement saying it was “committed to moving as many families out of the D.C. General shelter as quickly as possible” and devising a plan to close D.C. General and “provide alternative emergency shelter options.”

Currently, more than 600 families are in the city’s emergency shelter system. Though sub-freezing weather has likely ended for the year, thus freeing the city from its legal obligation to house them, the Gray administration has said it will keep the families sheltered until it can locate more permanent housing arrangements. Gray said Wednesday about 200 units have been tentatively identified for families currently in emergency system, including at D.C. General, whose management has come under new scrutiny in light of Relisha’s disappearance.

“It’s not a good place for children,” he said of the hospital-turned-shelter, which has housed upward of 900 in recent years. “Can you imagine an 8-year-old going to school or a 7-year-old or a 6-year-old or a 9-year-old and having to say … I live at D.C. General, in a shelter? No child wants to do that, and that is psychologically debilitating for a young person.”

But Gray, speaking at a Wednesday news conference, declined to commit to closing D.C. General by a certain date, saying the city would first need to establish a network of smaller emergency shelter units. And that, he said, is where the community opposition comes in.

“It is not a place that a child should be raised, clearly, but that’s unfortunately what we have available to us when we don’t get the cooperation of other leadership across the city to say, we will do our share to accommodate families,” he said. “We don’t want to use D.C. General, but we’ve got to have cooperation in establishing other facilities.”

No names were named, however — not even that of campaign foe and D.C. Council member Muriel Bowser, who pushed back on 2010 plans to locate additional shelter beds in her ward. And Gray did not know how many emergency units would need to be established — whether in community-based group homes or in other settings — to offset the capacity that would be lost by closing D.C. General.

“We’re working on that now,” he said.