For Buffalo residents, this might not be the best time to have a medical emergency.

The Common Council on Tuesday put off renewing a contract with Rural/Metro Medical Services, which handles as many as 34,000 emergency calls a year in the City of Buffalo.

Since a two-year extension on the company’s original 5-year contract with the city expired July 1, 2012, the ambulance service has been operating on a month-to-month basis.

However, lawmakers expressed concern at Tuesday’s meeting of the Common Council about the possibility of a strike by emergency medical technicians working for Rural/Metro. Teamsters Local 375 on Friday delivered a 10-day notice to the private company signaling the union’s intent to strike if progress is not made toward negotiating a new wage scale for its members who, the union said, are currently paid below the city’s living wage.

“Where I am very concerned is that if Rural/Metro goes on strike, do we have enough time and do we have a contingency plan to ensure that ambulances will be on the street,” said Ellicott Council Member Darius G. Pridgen.

“We’re talking about life and death. I think this has to be a front-burner issue. They’re talking about striking,” he added.

Rural/Metro Division General Manager Jay Smith said in a news release that the company is committed to negotiating a fair deal with its employees and that it planned to meet this week with a mediator and with union representatives in an effort to solve the contract impasse.

“First and foremost, we want to assure people that EMS coverage will continue and they can expect the same high level of medical care,” he said.

“It is the nature of the EMS industry to prepare for any variety of scenarios, and we are working closely with our partners in first response, health care and other Rural/Metro divisions to ensure uninterrupted service,” Smith said.

Pridgen and other lawmakers on the Council also expressed concern that EMTs working for Rural/Metro are not paid the same wage that is required when those first responders attend calls outside the city. Rural/Metro, which has a fleet of nearly 100 emergency vehicles, responds to about 125,000 emergency calls each year across the Niagara region, including Buffalo.

“The company that owns Rural/Metro is a private equity firm, Warburg Pincus, and it’s worth tens of billions of dollars,” said Fillmore Council Member David A. Franczyk.

“There’s people that have the lives of our citizens in their hands,” Franczyk said, referring to the EMTs who work for Rural/Metro. “Yet they pay you chump change to save a life,” he added.

North Council Member Joseph Golombek Jr. raised concerns about response time in light of a Riverside Avenue fire in the city’s Riverside neighborhood that claimed the life of a 6-month-old boy early Tuesday.

“What I’m hearing right now, and I’m especially concerned about this, is that it took somewhere between eight and 10 minutes before the ambulance actually showed up. Sadly, by the time the Fire Department was there within the four-minute response time, which is an average response, the child had already passed away,” Golombek said.

“I would ask my colleagues to please send this to committee, please invite Rural/Metro in and have Rural/Metro be held accountable for the low wages that they’re paying their employees, but especially the poor service that they’re giving to the residents of Buffalo,” he added.

The Council on Tuesday voted to send the matter to the Finance Committee so that lawmakers can meet with the city Law Department and members of the Emergency Services Board, which oversees ambulance service in the city.