D.C. Council members voted Monday to deny Mayor Vincent C. Gray’s proposal to include controversial changes to the city’s homeless law in his budget for the upcoming fiscal year.

Instead, council member Jim Graham (D-Ward 1) introduced the identical reforms as separate legislation and will hold the first public hearings June 3.

“The mayor was proposing major changes in the Homeless Services Reform Act without any opportunity for public input,” Graham said. “We all had the same reaction. There’s probably some good things in there, probably some not so good. But let’s have a public process.”

The proposal by Gray (D) sought to give homeless families “provisional” placements in shelters, require them to move into their own apartments with a temporary rent subsidy and mandate that they save 30 percent of whatever income they receive, including welfare benefits, in a savings account.

Advocates, including families from the homeless shelter that used to be D.C. General Hospital, testified before council members that the move would make it harder for families to get into shelters and easier to get kicked out.

City officials, faced with a burgeoning homeless population and crowded shelters, said the current system encourages dependence. Moving the homeless into permanent housing, they said, would get people on their feet faster and save the city money.

Without the reforms, they warned, they will have to close some shelters that now operate year-round and open them only on cold nights.

At issue is the city’s “rapid rehousing program,” which gives families temporary help paying rent. Officials say that it is a path toward stability; 91 percent of those who have through the program remained in stable housing a year later, they say. But homeless families and their advocates fear that after rental assistance ends, the homeless won’t be able to afford the steep market rates for rent.

“No one wants to stay here. It’s not a good place,” said Jordan Love Smith, referring to the D.C. General family shelter. After losing her job in a dental office in the fall, she bounced around on friends’ couches, lived in her car and slept on boxes in the back of a store before getting a bed at the shelter in March.

“But people don’t want to jump out in something and then be homeless again when they end up in an apartment that’s overpriced and then, after a year, they can’t pay for it anymore,” Smith said. “When you go through homelessness, it hurts. People are scared it’s a setup.”