A Richmond city councilwoman is calling on the School Board to halt its effort to retake control of school construction and to come to the table with city officials “to create a process that everyone can support.”

Fifth District Councilwoman Stephanie A. Lynch issued the call Wednesday in a bid to end the growing rift between City Hall and the School Board over development of a replacement for aging and decaying George Wythe High School, which the city had hoped to build and open by the fall of 2024.

However, Ms. Lynch, who chairs the council’s Education and Human Services Committee, said that if the School Board does not accept the olive branch and rescind its action, she said she would recommend that Mayor Levar M. Stoney and his staff ignore the board and move ahead with issuing requests for proposals, or RFPs, for school buildings that the city has been preparing, given the city’s control of the purse strings.

The contention began April 12 when a divided School Board voted 5-4, without any public notice, to retake control of school construction. The board had ceded school construction to the city in the development of the seven newest buildings that have gone up since 2012.

The board’s action has drawn fire from civic groups and community activists.

But just hours after Mayor Stoney spoke at a news conference Monday urging the School Board to back off, the board doubled down. The same five-member majority directed Superintendent Jason Kamras to begin the process of hiring a three-member construction management team and also directed him to develop and issue RFPs for George Wythe and a modern career and technical center this year.

The majority on this issue includes School Board members Kenya J. Gibson, 3rd District; Shonda Harris-Muhammed, 6th District; Stephanie M. Rizzi, 5th District; Mariah L. White, 2nd District; and Jonathan M. Young, 4th District.

The four other board members, Liz B. Doerr,1st District; Cheryl L. Burke, 7th District; Dawn C. Page, 8th District; and Nichole Jones, 9th District, have been adamantly opposed.

The April 12 action halted City Hall’s plan to issue RFPs before the end of April for replacing the George Wythe building and installing the new technical center in a former tobacco factory on South Side that Altria donated to the school system several years ago as part of a new partnership with Reynolds Community College. Reynolds is to operate the center.

The creation of both schools are priorities for the city and the School Board.

The board’s sudden intervention shocked and dismayed Ms. Lynch, who has been pressing Mayor Stoney and his staff to step up the pace of developing and issuing the RFPs, particularly for George Wythe, which is in her district.

“We cannot tolerate any delay in getting a new school built,” Ms. Lynch said. “As an elected representative, and as a parent of a student who will have to take classes in that decrepit building, we need swift action.”

In issuing her call, Ms. Lynch acknowledged, based on a new opinion from Attorney General Mark R. Herring, that the School Board can control school construction. However, as the board has no independent funding source, she also noted that the School Board could not proceed to develop any new buildings without council including money for that purpose in the school’s budget.

“That’s not going to happen,” she said.

No such request, though, was included in the fiscal 2021-22 budget that is being wrapped up ahead of the July 1 starting date. As a result, any such request could not be considered before next spring during deliberations on the 2022-23 fiscal year budget. “That would automatically delay everything for at least a year,” Ms. Lynch said.

Ms. Lynch has scheduled a special session of her committee for Thursday, April 22, to hear testimony from Mr. Kamras, who has warned the board it likely would need to hire 15 new staffers at a cost of $3 million and should expect development of a replacement George Wythe to be delayed until 2027.

She said if the School Board gives up its quest to control construction, the school system still would be in charge of building design and public engagement and would be included on the city’s construction team. But she said the board currently lacks the capacity to handle the work and should not spend money to duplicate functions that the city already has in place.

Mayor Stoney used Monday’s news conference at the George Wythe building to also urge the board to reconsider, citing the success of the city-school partnership in the development of the new Cardinal and Marsh elementary schools and River City Middle School.

“What we have proven, when working together, is that we do get things done,” Mayor Stoney said.

He reminded of his promise last October, ahead of his re-election, “that we were going to build a new George Wythe before 2024.”

Corey Stuckey, a senior at George Wythe, recalled that the building has been on the list for replacement since 2002 — before he was born —“and it is still not done.”

“It’s time for us to act. I don’t want to hear anything else until an action is attached to the promise,” said Mr. Stuckey, a founder of the 381 Movement. “I don’t want to hear George Wythe is being rebuilt unless it is actually being rebuilt.”

Seeking to keep the pressure on, Mr. Stuckey called on people who support a replacement of George Wythe to join him at 1 p.m. Friday, April 23, for a march from the Maggie L. Walker statue at Adams and Broad streets to City Hall.