City officials on Tuesday offered raises and a health care package to the San Antonio Professional Fire Fighters Association at a collective-bargaining session that union officials did not attend.

Later in the day, union boss Chris Steele rejected the idea that the city could even issue a proposal because the firefighters’ negotiating team had yet to agree to come to the bargaining table.

The city’s proposal for a four-year contract includes a total of 4 percent in one-time lump-sum payments and 8 percent increases to salaries. It would require for the first time that firefighters pay monthly health insurance premiums for spouses and dependents, but they would continue to receive coverage without premiums for themselves. And the deal would include a reduction of the controversial “evergreen clause” from 10 years to six months.

It’s the latest turn in a saga that began even before the union’s labor contract expired in 2014.

Steele has said repeatedly he will not negotiate until the city drops its evergreen lawsuit. Challenging the constitutionality of a clause the city has continually agreed to, city lawyers lost their battle at district court and on appeal but remain confident that the Texas Supreme Court will overturn the lower courts.

City spokesman Jeff Coyle said Tuesday that officials don’t expect a court resolution until next year; Steele said he thinks it will be resolved by this summer.

Shortly after 10 a.m., when the collective-bargaining session was set to begin, Deputy City Manager Erik Walsh, City Attorney Andy Segovia and other members of the city’s negotiating team were seated at a conference table on the first floor of City Hall. Coyle stood nearby, presenting the city’s offer to a gaggle of reporters.

“Thank you all for being here again today,” Coyle said to the TV cameras. “This is the collective-bargaining session between the city of San Antonio and the San Antonio Professional Fire Fighters Association. As you can see, the fire union is not here again today, and we’re disappointed by that, but we’re glad that you are because we are prepared to make a proposal — the outline of a proposal — to the union for their consideration.”

The city’s proposal would eliminate funding for a police and fire legal fund — which pays legal fees for things like probate, wills and divorces.

Under the deal, firefighters would receive a 3 percent lump-sum bonus when a new contract is signed. The next year, they’d receive a 1 percent bonus and a 2 percent recurring wage increase. In the third and fourth years, they’d have 3 percent salary increases. Over the four-year offer, they’d see a total of 4 percent in lump-sum, one-time payments and 8 percent in wage increases.

Firefighters would pay about $346 monthly to insure a spouse and children. To only insure a spouse, they’d pay about $208 monthly or $139 for children only. Their annual deductibles would remain low: $654 for an individual and $1,308 for families with maximum out-of-pocket expenses, including deductibles and copays at $2,482 and $4,946.

Coyle said he wasn’t sure whether the offer would leave firefighters with more or less money in their pockets. But Steele said the offer is the same one the city put on the table during failed court-ordered mediation last year and that he believes it’s a net negative.

“That’s not the first time I’ve seen that proposal. That was rejected in mediation,” he said in a Tuesday interview. “My guys would take a financial loss.”

Mayor Ron Nirenberg said Tuesday that he hopes Steele would counter the city’s proposal.

“I think this is a fair offer,” he said. The mayor said the health care premiums are lower than any other city employees’ and that of “virtually every member of the private sector.”

“That being said, I understand the concern about being upside down. If it actually exists, we would only be able to determine that at the negotiating table, and there would be a willingness, I’m sure, for us to work on that.”

There is not a willingness, however, to drop the lawsuit.

But there is an offer that might sway Steele to change his mind.

He’s suggested the union should take over health care management using an annually allocated amount based on a percentage of firefighters’ salaries. The union would create a plan and members would contribute to their health care costs.

It’s a proposal that’s been rejected as many times as it’s been offered. Officials say the city ultimately is responsible for insuring firefighters if the union’s plan is a bust.

Steele’s offered a remedy to that. He’s so confident that his association can manage its own health care that he’s given the city a clawback that should have made municipal officials salivate.

“We said if it does not work, and we raise the white flag and say ‘I’m sorry it’s not working,’ we will go on the civilian plan — not the police plan — the civilian plan,” he said. “We made it no risk, a no-brainer in mediation, and they said no.”