The Montgomery County Council all but completed its work yesterday on a fiscal 1984 budget that is expected to exceed $776 million and may require a property tax increase to help pay for it.

With a deadline of Monday for final ratification, the seven often-bickering council members have already approved budgets for the county's largest departments and agencies, in most cases accepting County Executive Charles W. Gilchrist's recommendations.

The only major exceptions have been the public schools budget, where the council increased Gilchrist's request by $3 million for a total of $370 million, and the budget for the park and planning commission, which got an $800,000 increase over what Gilchrist wanted, for a total of about $23.8 million.

Those two large increases are expected to necessitate a tax increase, unless the county's revenues exceed current projections, said Jacqueline H. Rogers, Gilchrist's budget director.

The council, which met into last night on the budget's last items, including the recreation department and the council staff, also cut a few items from what Gilchrist recommended. For example, council members trimmed $200,000 from the police department's proposed $49 million budget, the bulk of which will come primarily out of the department's budget for ammunition.

The only acrimony between Gilchrist and the council during this budget cycle came over a decision by the council's majority faction to cut a position from the county attorney's office. Four council members--who ran on a Democratic Party slate opposite Gilchrist in last year's primary--complained that the county attorney, a Gilchrist political appointee, often delivered adverse or inadequate legal opinions to the council.

Gilchrist blasted the council for cutting the position, calling it "a vindictive action." Yesterday, council member William E. Hanna Jr. shot back that Gilchrist had engaged in "an intemperate outburst," and accused the executive of "a personal attack of tragic proportions." A half-hour debate ensued, reminiscent of preelection squabbling, with Gilchrist's three political allies lining up to defend him and the four-member majority criticizing the county attorney's office and defending the cut.

This year's budget debate has been less frenzied than past sessions, which often found the council up against deadline with major items still unresolved. This was the first test of Council President David L. Scull's new committee system, which now divides the budget among seven three-member committees. In the past, individual council members met with individual department heads to review sections of the budget.

The committee system won praise from Rogers, who said she found it easier to work with.