Officials at San Francisco Unified School District may have acted prematurely in raising wages for around 3,600 teachers before the revenue stream to pay for them — generated by a parcel tax voters approved in June — actually kicks in.

In a letter sent to SFUSD Superintendent Vincent Matthews on Friday, Mayor London Breed called the timing of the wage increase an issue of “great concern,” given unresolved questions about when the money generated by Proposition G will be available, or if it’ll be available at all.

That could mean that the school district is spending money to raise teacher wages while anticipating revenue that might never materialize.

SFUSD teachers have been receiving bigger paychecks since late August, according to Laura Dudnick, a spokeswoman for the district.

Prop. G sought to provide a $5,500 boost to teachers’ salaries by levying a $298 annual parcel tax, which would generate around $50 million a year. The measure passed with nearly 61 percent of the vote.

Breed, who supported the parcel tax, said in her letter to Matthews that she still believes “our educators deserve better pay for the important work they do every single day to educate and support our children and families.”

Yet she questioned the “fiscal prudence” of raising wages before the money generated by the measure has even been collected.

Dudnick said in an email that “SFUSD is taking steps to develop contingency plans to protect the financial well-being of the district without creating risk to the city and county. In the meantime, we are intending to continue in processing the raises.”

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She added that both the school district and United Educators of San Francisco, the teachers’ union, “agreed that it was important to implement the measure as soon as possible, in order to attract, recruit, hire and retain educators for this school year.”

Susan Solomon, president of UESF, said the raises were helping with the district’s recruitment efforts and had lifted the morale of existing staff.

“In general, we’ve heard from many of our members about how respected they felt and how happy they were to see the raise,” she said, adding that the union had “no expectation” that teachers who received raises would have to repay them.

The first property tax mailings that would include the Prop. G parcel tax have not yet been mailed to homeowners, Breed said, and the first payments on those taxes aren’t due until December. On top of that, both Breed and the Board of Supervisors have to approve and transfer the funds once they’re collected.

“Neither body has appropriated and transferred SFUSD any funds for this purpose,” Breed said.

But a legal challenge to another June ballot measure could pose an even greater threat to Prop. G. Last month, the Howard Jarvis Taxpayers Association sued the city to block it from implementing Proposition C, which sought to raise commercial rents to fund a variety of child care and education initiatives. Prop. C narrowly passed with just under 51 percent of the vote.

Calling Prop. C an “illegal special tax,” the Jarvis association sued, claiming that because Prop. C was levying a tax for a specific purpose, it required a two-thirds majority to pass, according to state law.

In 1996, California voters approved Proposition 218, which spelled out the procedures for how local governments can levy new taxes and fees, including the vote thresholds that have to be met to approve proposed taxes. Since then, taxes for a specific purpose have required a two-thirds majority to pass.

But a memo written by the San Francisco city attorney’s office last year interpreting a state Supreme Court ruling argued that proposed tax measures placed on the ballot by citizens — and not the government — needed only a simple majority to pass.

Now, the fates of Prop. C and, by extension, Prop. G. are tied to the outcome of the Jarvis lawsuit. If the court is convinced by the Jarvis association’s arguments, it would probably prevent both measures from being enacted. The case also has implications for November’s “Our City, Our Home” ballot measure, which is also seeking a simple-majority vote to pass a tax on commercial gross receipts to fund homeless services.

The City Controller’s Office, Breed said in her letter, had also informed the school district that “current legal uncertainties” prevented the city from authorizing Prop. G funds to boost teachers’ pay.

The district’s actions, Breed said, “during this time of uncertainty, and unresolved legal circumstances regarding the allocation of funding under Proposition G, give me great concern about the fiscal prudence of this decision.”

Dudnick, the school district’s spokeswoman, said SFUSD looked forward to “discussing the issues” with Breed. Solomon from the teachers union said that should the courts rule against the city, “we would go back to the table with the school district and discuss what would happen moving forward.”

“The district has also been in conversation with the controller’s office for several months about the intentions of SFUSD and plans to distribute the Prop. G funds without creating risk to the City and County,” she said.

Dominic Fracassa is a San Francisco Chronicle staff writer. Email: dfracassa@sfchronicle.com Twitter: @dominicfracassa