Richmond Mayor Levar M. Stoney’s honeymoon with Richmond City Council appears to be coming to an end.

Asserting that the council needs greater control over spending, two of the newest members, Kim B. Gray, 2nd District, and Kristen N. Larson, 4th District, are planning to introduce legislation that would slap fiscal handcuffs on the mayor and his administration.

If approved, the ordinance would impose limits on the ability of the mayor and his administration to make spending decisions without consulting with and gaining the approval of the council.

In some ways, the proposal addresses concerns that became epidemic under former Mayor Dwight C. Jones. Council members frequently fumed during the Jones era that he kept them in the dark and waited until the last minute to seek their approval on everything from big development projects to the budget.

But even in his first few months, Mayor Stoney and his administration have been losing fans on the council. During the council budget sessions, members complained that they were being forced to make decisions with incomplete or inadequate information.

For example, Councilman Andreas D. Addison, 1st District, was critical of the information he received from the administration about vacancies at City Hall that failed to distinguish between positions backed by funds and those that were not.

Councilman Michael J. Jones, 9th District, repeatedly pilloried the administration for forcing council to find funds to fill critical positions that were left unfunded in the mayor’s budget plan. He said the administration should have provided more disclosure to the council about the personnel needs that could not be met.

Meanwhile, the mayor and his staff has given the green light to the Department of Public Works to spend extra money to fix alleys and mow grass, projects that have been started even before the mayor seeks the council’s approval.

“Maybe that is not the way we would have decided to spend the money,” Ms. Gray told her colleagues.

The conflict over how the mayor wants to spend money and how council would is among the reasons that the Gray-Larson proposal could garner the required five votes to stick.

The proposal that Ms. Gray and Ms. Larson plan to introduce to council, possibly as early as Monday, May 8, would transform the budget from a flexible planning document that the administration can adjust at will into a concrete slab.

The proposal would bar the administration and every department from exceeding the total appropriated “without an amendment approved by City Council prior to initiation of the expenditure,” except in the case of emergencies, according to a statement of principles Ms. Gray has distributed.

That would be a sea change for City Hall. Typically, some departments overspend and some underspend their budgets. For example, the Sheriff’s Office may have unexpected medical expenses for inmates, or the Police Department may spend more on overtime than anticipated.

Other departments may buy fewer supplies or a director might be tight-fisted and end up spending less to show it can be done.

Next week, Mayor Stoney is expected to introduce a paper to the council that would enable his administration to shift around departmental dollars to deal with excess spending. Transfers between departments now require council approval.

Last year during former Mayor Jones’ tenure, Councilman Parker C. Agelasto, 5th District, expressed concern that council was receiving the ordinance to reconcile departmental spending just a few weeks before the end of the fiscal year, with too little time to give it careful review.

He urged then that the administration in future years bring the information and the explanations sooner to the council so it could get more scrutiny.

The administration, led by Chief Administrative Officer Selena Cuffee-Glenn, failed to heed his advice, but now there are more on council who agree with Mr. Agelasto, including Ms. Gray and Ms. Larson, who began their first terms on council in January.

Like him, they do not believe that the administration should be allowed to come in at the last minute and force the council to agree to the administration’s spending decisions.

The new ordinance, if approved, would bring that practice of spending and then seeking council’s approval to a screeching halt. Advance permission would be required for a department to go over budget, unless it was an emergency.

The Gray-Larson proposal also would require council approval for changes within a department as well.

Department directors have long been allowed to move money from one program to another as long as they did not exceed their total appropriation. The Gray-Larson proposal would require council permission that would increase or decrease spending on a program by more than 5 percent.

Whether or not the ordinance is approved, the proposal is a warning shot and indicates that the council, as the city’s governing body, is seeking to make clear that it has no interest in taking a backseat to the mayor.