Massachusetts lawmakers on Monday approved the release of $20 million in heating aid for low-income households as the long, cold winter drags on — the first time in three years that the state has provided such assistance.

The money, included in a supplemental spending bill, received final approval from the Senate in a voice vote Monday. Secretary of State William F. Galvin signed the bill into law as Governor Deval Patrick was out of state, on a trade mission in Panama and Mexico.

The money is crucial for tens of thousands of poor households that have struggled to keep the heat on since about mid-January, when the state exhausted $140 million in federal heating aid. About 200,000 Massachusetts households rely on the government to help them keep their homes warm each winter.

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Advocates for the poor estimate the state money will mean an additional $100 per eligible household to help offset some of the highest heating bills in years. New England residents are projected to pay an average of $1,700 to heat their homes, up nearly $300, or 20 percent, from last winter.

Senator Stephen M. Brewer, chair of the Senate Ways and Means Committee, said the need some Massachusetts families have found themselves in this winter in was driven home when he got his most recent oil bill, $803.

“I gasp, and I thank the lord I have the ability to pay my bill,” said Brewer, Democrat of Barre. “What happens to the people who are on fix incomes, or low-income, and are making choices between food in their refrigerator or medicine in their medicine cabinet, and fuel?”

Federal heating assistance has traditionally helped, but the program has been cut by one-third in recent years, to $3.4 billion this year from $5.1 billion in 2010. In the past, Congress supplemented the program with additional money during the winter, but the last time that happened was 2010.

Senate President Therese Murray said the funding will help reduce the burden on Massachusetts’ most vulnerable residents.

“This has been one of the coldest winters in recent memory and even halfway through March the temperature is still below 30 degrees,” Murray, a Plymouth Democrat said in a statement. “The already high cost of energy continues to rise and many families are struggling to make ends meet.”

Low-income advocates have spent the last several months pushing Massachusetts lawmakers to provide funding for heating assistance.

“We’ll be very glad to get that $20 million,” said John Drew, president of Action for Boston Community Development, an agency that helps funnel heating aid to families in Boston, Brookline, and Newton. “We wish it had come earlier.”

Still, Drew said he is worried about natural gas and electric customers who have wracked up enormous heating bills this winter and will soon be receiving shutoff notices from their utility companies. State law prevents utilities from shutting off service to customers between Nov. 15 and March 15, even if they fall behind on payments

Galvin on Monday called for the shutoff moratorium to be extended until at least April 15. “There’s a real hardship out there,” Galvin said. “I think a lot of people who never expected to be in this predicament are.”

The state’s investor-owned utilities already have agreed to extend the moratorium until April 1, at the request of state regulators. National Grid spokeswoman Deborah Drew said her company also agreed to use the April deadline in future years, too.

Northeast Utilities next month will start sending out shutoff notices to affected customers of its Massachusetts subsidiaries, NStar and Western Massachusetts Electric Co, said spokeswoman Caroline Pretyman. They won’t be disconnected from service until May 4.