The number of Gateway Cities would increase by 33 percent if two separate amendments tweaking the qualifications become law, the Patrick administration says.

Gateway Cities are currently defined as cities with a population greater than 35,000 but less than 250,000, a median household income below the statewide average, and a rate of educational attainment of a bachelor’s degree or higher that is below the state average. Currently, 24 cities fall under that definition, entitling them to state grants and support for economic and community development.

A provision contained in the proposed Senate budget would lower the population threshold to 20,000, paving the way for Falmouth, Gardner, Yarmouth, Wareham, Gloucester, Agawam, and West Springfield to become Gateway Cities. A provision in the House jobs bill would tweak the median household income requirement and allow Attleboro to qualify.

Officials in Gardner and Attleboro have led the charge for the changes, which are opposed by Rep. Antonio Cabral, a New Bedford Democrat who co-chairs the Gateway Cities Legislative Caucus. Cabral says the expansion would dilute the impact of the Gateway Cities funding by stretching a limited amount of funding over a larger group of municipalities. Patrick administration officials are declining to say where they stand on the amendments.

Attleboro Mayor Kevin Dumas said the Gateway Cities designation would allow companies in his town to qualify for tax credits, helping them stay in the city. He sees no downside from expanding the program. “I think more of the former mill cities should be allowed to go through the program,” he said. “We should be able to have that opportunity.”

The Gateway Cities designation has also become an issue in the race for state representative in Attleboro, with Republican Rep. George Ross facing pressure from his Democratic opponents to move Attleboro into the program. Democrat Steven Kane said it would be a top priority for him if he is elected.

Officials in some of the other cities that might qualify as Gateway Cities if the law changes had only limited knowledge of the program.

Peter Johnson-Staub, the assistant town administrator in Yarmouth, said he was unaware that the Senate amendment included Yarmouth but was thrilled with the news. According to Johnson-Staub, Yarmouth hadn’t been pushing aggressively for the change.

Johnson-Staub said his only information about the Gateway Cities program came from reading articles in Commonwealth. After reading Gardner Mayor Mark Hawke’s commentary in the Winter 2012 issue, he saw potential for his own community. He said his town of about 24,000 has some depressed areas, littered with vacant houses and storefronts. “The town will take “any resources that we can get to revitalize these distressed corridors,” Johnson-Staub said.

Falmouth Town Administrator Julian Suso also said he wasn’t very familiar with the program but could see benefits for his town. “I think the concept of a Gateway City, based on my modest understanding of it, is a city that occupies a geographic position of some prominence,” Suso said. “It makes considerable sense to me that Falmouth would have a designation like this.”