Keeping consistent with its search for alternative solutions to lower Boston’s rising violent-crime rate, the City Council proposed a new sales tax yesterday that would go directly toward Boston’s safety budget.

Councilor-at-Large Sam Yoon proposed the city levy an additional five-cent sales tax on every $10 spent in Boston, which he estimated would amount to almost $35 million per year toward a public-safety fund for the city’s crime-fighting efforts.

Nearly every municipal agency is struggling with a budget shortfall, he said.

“We need to create more sources for revenue in the city,” he said. “This is one of them.”

Though Councilor-at-Large Felix Arroyo, Councilor Michael Ross (Back Bay, Fenway) and Councilor Salvatore LaMattina (North End, East Boston) said they back the measure, others said they worry the tax would have a negative impact on the local economy.

Councilor Chuck Turner (Roxbury, Dorchester) said the city needs to do more to stem the violence of past months — the Boston Police Department lists 19 homicides to date in 2007 — than simply hiring more police, but cautioned that the city should investigate the additional burden such a tax would weigh on Boston’s poorest, already struggling with a high cost of living.

“We don’t want to overburden the lower-income and working-class families,” he said.

Councilor Charles Yancey (Dorchester, Mattapan) also suggested the city look elsewhere for increased funding.

“We need to dig a little deeper,” he said. “How can we have a progressive approach other than a sales tax?”

Council President Maureen Feeney (East Boston, Harbor Islands) said the idea requires several more hearings to examine if it is fair and feasible.

“We need to take the temperature before moving forward,” Feeney said. “Make sure the money [would be] going to effective resources.”

The matter was referred to the Committee on Government Operations, and if it is approved at a future hearing, Mayor Thomas Menino will have to sign off on it.

Councilor-at-Large Michael Flaherty also proposed the city hire 80 additional Emergency Medical Technicians to support what he said is a currently overworked service that must respond faster to underserved areas. Together, Boston EMS and paramedics respond to about 150,000 calls a year, he said.

“If it wasn’t for EMTs in Boston, the death rate would be double what it is now,” Flaherty said. “They’re underappreciated, quite frankly.”

Councilor Jerry McDermott (Allston, Brighton) backed Flaherty’s proposal, saying the high number of senior citizens who live in his district is taxing to the service.