The D.C. Council overruled Mayor Vincent C. Gray (D) on Monday and eased proposed penalties for welfare recipients who refuse job training, but they will still risk some benefits if they don’t learn how to become self-sufficient.

As part of an ongoing debate about how to alter the District’s lenient public-assistance polices, the council voted 11 to 2 to modify rules that will help limit welfare benefits to five years.

A strong majority of council members were concerned that some of the city’s policies would in effect punish poor children for the behavior of their parents.

The changes to the Temporary Assistance for Needy Families (TANF) program will require recipients to get individualized counseling on how to gain skills to find work within 60 months so they can be independent when the TANF benefits end. The modifications are set to take effect this month.

Those who do not complete the counseling will face escalating sanctions, including a one-month suspension of benefits. The council removed the toughest measure, which would have resulted in a loss of at least three months of benefits.

Council member Jim Graham (D-Ward 1) said 31,000 children benefit from the TANF program.

“They have been tough issues for the District of Columbia because D.C. has a heart and the D.C. Council has a heart,” Graham said. “We care deeply for the most vulnerable. We are talking about $336 [a month] for a single parent and a baby, and to take that away would have devastating impact.”

The vote exposed the limited influence of the council chairman, Phil Mendelson (D), who had urged his colleagues to back all of the Gray administration’s proposed sanctions. Mendelson said the council’s decision could make the new regulations meaningless.

“It is important to help people on welfare, but we help them by getting them jobs,” he said. “The sanctions are so they become able, get jobs. . . . We don’t help these folks if we say, ‘Hey, we got a plan for you, but we are not serious if you don’t follow the plan.’ ”

The vote occurred during the council’s first meeting of the 2013 session. Members introduced more than two dozen bills.

The council will consider proposals this year to extend the city’s $12.50 hourly living wage to large retailers, rewrite campaign finance laws, legalize surrogacy agreements, establish a domestic-violence hotline and mandate that vending machines in city buildings contain more healthy food.

In one of its first acts, the council unanimously approved an emergency resolution calling on President Obama to put D.C. “Taxation without representation” license plates on the presidential limousine.

Former president Bill Clinton agreed to the symbolic gesture in the 1990s, but Obama has declined, to the annoyance of the council.

“We have been for so long abused,” said council member Mary M. Cheh (D-Ward 3), sponsor of the measure to encourage Obama to outfit his limousine with the plates before the inauguration.

But much of the session centered on how best to implement the guidelines for counseling the nearly 17,000 families in the TANF program.

Under federal welfare reform measures approved in 1996, states were encouraged to limit benefits to five years. District officials resisted the change, arguing that the city couldn’t guarantee that recipients were receiving adequate training and counseling.

After Gray was elected in 2010, he and the council broadly agreed to begin enforcing the five-year limit. In April 2011, the council voted to cut benefits by 20 percent for people in the program more than five years. The measure is scheduled to take effect in April, administration officials said. The cuts have been on hold while the Gray administration crafted rules for individual assistance plans.

Last month, Graham and council member Marion Barry (D-Ward 8) asked the council to scrap most of the mayor’s proposed sanctions. The Committee on Human Services rejected the idea, instead approving the scaled-down legislation that was passed Monday.

Mendelson and council member David A. Catania (I-At Large) opposed the bill, arguing that the city government should be more strict about reducing welfare dependency.

“Hiding behind children and allowing adults to continue bad behavior is not going to help the children,” Catania said.