BOSTON — State lawmakers are plodding ahead with plans to nix a controversial rule that denies benefits to children conceived to families receiving public assistance.

On Tuesday, the House approved a budget amendment to lift restrictions that advocates say affect nearly 9,000 children living in poverty.

At least 87 representatives — more than half of the House — backed the amendment.

“Most states have gotten rid of this cap, which is hurting children and families that need state assistance,” said Rep. Paul Tucker, D-Salem. “This policy was enacted in a punishing way and never should have been put in place to begin with.”

If the measure survives budget negotiations, changes would go into effect July 1, 2019, and the state would need to come up with an additional $13 million. The amendment didn’t increase the budget to cover the added costs.

The number of families on the state’s primary cash benefit program, known as Transitional Aid to Families with Dependent Children, fluctuates slightly every year. Overall, the number has declined substantially since the 1990s to about 29,000 in April, according to state data.

The state now spends about $16 million a month on the program.

The amount of help a family may receive is based upon its size. A mother of two can get up to $578 a month, as well as a yearly clothing allowance of $300 per child, according to the Department of Transitional Assistance, which administers the program.

If a child is born while a family gets benefits — or within several years of receiving state assistance — the family gets $478 and no clothing allowance for the newest child.

Massachusetts is one of 17 states — including Arkansas and Mississippi — that cap welfare benefits for families which have additional children while on public assistance, according to the National Conference of State Legislatures.

At least seven states have repealed the caps in recent years.

Advocates for the poor have been prodding the state for years to lift the cap, which was enacted as part of welfare reforms in the mid-1990s.

Naomi Meyer, a senior attorney at Greater Boston Legal Services and member of the Campaign to Lift the Cap on Kids, said the restrictions are discriminatory and force parents struggling to find work and housing to forgo basic necessities.

“It forces them to choose between buying diapers and paying bills,” she said. “Women on welfare aren’t having babies to get an extra $100 a month.”

Christian M. Wade covers the Massachusetts Statehouse for North of Boston Media Group’s newspapers and websites.

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