The Orleans Parish Sheriff’s Office says it needs another $3.5 million to keep the city’s jail running through the end of the year, including an emergency cash infusion to make its next payroll.

The request from the Sheriff’s Office will be hashed out at a special City Council meeting Tuesday morning, just before council members take up the equally contentious matter of Sheriff Marlin Gusman’s budget for next year.

In a letter he sent last week, Council President Jason Williams called on the Sheriff’s Office to come to the meeting with detailed budget documents laying out exactly where the money it has received so far has been spent.

Budgetary conflicts have been a major flashpoint that has seen Gusman repeatedly facing off against Mayor Mitch Landrieu’s administration and a majority of the City Council.

City officials have said the jail, which the city is required to pay to operate, could be run more cheaply. They have used the high cost of incarcerating inmates as an argument against building an additional lockup that would hold several hundred more inmates, as Gusman wants.

The Sheriff’s Office has countered by pointing to the cost of implementing the federal consent decree governing the jail’s operations and the unexpectedly high cost of running the newly completed facility. It also has argued that the emergency funding would not be necessary had the city gone along with its initial budget request.

Last year, Gusman asked the council for $66 million for 2015 but received only about $28.6 million in the budget approved last November. The council has been adding money to that pot in a piecemeal fashion throughout the year.

The council will consider two measures at Tuesday’s meeting. One, already approved by the council’s Budget Committee, would boost funding to the Sheriff’s Office by $2.8 million, an amount the city has largely consented to provide. In addition, the Sheriff’s Office has now said another $3.5 million is necessary to cover the cost of furnishings and equipment at the new jail needed to meet the standards set out by federal monitors, plus other unexpected items.

If those two measures are approved and no more money is needed this year, the city will have allocated a total of about $53.5 million to the Sheriff’s Office over the course of 2015.

The Landrieu administration’s proposed budget for the coming year includes about $44 million for the jail, which the Sheriff’s Office has said is about $15 million less than it needs. Those figures will be debated by the council and Sheriff’s Office during Tuesday’s hearing, the last in a series of budget meetings the council has held in the run-up to a vote on a final budget on Thursday.

Follow Jeff Adelson on Twitter, @jadelson.