Despite warnings earlier this year of an increased property tax rate and widespread cuts in county programs, Prince George's County Executive Winfield M. Kelly Jr. proposed a county budget yesterday that would leave the tax rate unchanged and finance many of the projects the executive had said might be eliminated.

Kelly's proposed $418.6 million budget would keep the county tax rate at $3.37 per $100 of assessed valuation. The budget calls for a 6.6 per cent increase in county spending - about the same rate at which expenditures have increased over the three previous years of Kelly's administration.

Maintaining the same property tax rate does not mean Prince George's homeowners will avoid higher property taxes this year. Most can expect bigger property tax bills because of rising assessments.

And in keeping the size of the budget down, Kelly calls for cutting the spending proposals of several departments, including schools, libraries and police. That could lead to reduced services and seems sure to generate controversy.

In January, Kelly painted a grave, stark and pessimistic picture of the county's financial future, predicting that the property tax rate would have to be raised by 26 cents per $100 unless the state legislature granted the county additional taxing authority.

The response to Kelly's plea by the county's legislative delegation to Annapolis was proposed "home rule" legislation that would enable the County Council to impose a 15 per cent tax on telephone bills that would produce about $5.2 million in revenue. The bill is still pending, but chances for its passage are considered good.

Kelly aide John A. Lally said that without keeping budget growth to a minimum and without "the help from the (legislative) delegation, we would have had to raise the property tax."

Kelly also said last January he would suspend new construction projects - such as clinics and libraries - because the county could not afford to pay the interest on construction bonds.

The county executive said yesterday that with the change in the financial picture, he could go ahead and sell $16 million of the $26 million in bonds he had cut earlier. Just by delaying the sale of those bonds, Kelly contended, the county was able to save about $1.3 million in interest payments.

Kelly said he had not yet decided which projects would be funded through the bond sale, but said "many . . . will be those that were deferred in December."

Kelly said he considers an ambulatory care center for Bowie, the first step in the construction of a county-run hospital for that municipality, "a priority."

Kelly's budget also includes $940,000 in special grants to be distributed among the county towns that supply residents certain services, such as street-lighting, police protection and garbage collection, which the county normally would provide.

Last January, when Kelly was painting a much gloomier picture of county finances, he had threatened to eliminate the credit to municipalities from fiscal 1978 budget.

Back then, Kelly also appeared pessimistic about the opening of the Laurel Hospital, but next year's budget includes $2 million to put the facility in operation.

A $3.3 million surplus in last year's Board of Education budget also helped to reduce the anticipated budget deficit, Kelly said.

According to school spokesman John Aubuchon, the surplus came from two main sources: a $1.1 million payment from the state for transportation costs it owed the country and a $2.1 million savings in teachers' salaries.

That savings was made possible, Aubuchon said, because of a drop in the number of teachers who qualified for raises through academic achievements.

According to Kelley, the balanced budget is also due in large part to tightening up the finances of the various county agencies and departments.With few exceptions, Kelly cut the budgets of the various departments or proposed only slight increases over allocations for the current fiscal year.

Among the hardest hit would be the Health Department, schools, libraries, police and public works and transportation.

The county has proposed a $10.3 million budget for the health department, $1.2 million less than the department requested, according to Dr. Donald Wallace, health officer.

Wallace said he may be forced to close some of the county's day-care centers for the mentally retarded. It is also likely, Wallace said, that the hours for treatment at mental health out-patient clinics will have to be curtailed.

School Board Chairman Jesse J. Warr Jr. called the executive's proposed $245.8 million school spending proposal "shocking." Kelly is proposing $5.3 million less than the school board has requested.

The school board's budget requests, Warr said, "were really down to earth, with no frills. We were only trying to maintain present conditions." Warr said that by proposing a "bare-bones school budget," Kelly may force the school board to reduce the number of teachers.

The Prince George's library system would suffer one of the severest budget cuts, resulting in the possible closing of branches in College Park, District Heights, Bladensburg, Magruder, Mount Rainier and Suitland and the reduction of library hours.

Kelly has proposed adding no members to the police force and reduced the police budget by $468,813. The police and fire departments are the only departments where a hiring freeze is not in effect.

Nonunion county employees can expect a 5 per cent salary increase next year.

About $3.5 million of the revenue Kelly anticipates to fund the budget would come from a change in the state's aid to education formula that is being sought by the county's legislative delegation. Enactment of the change is no tconsidered certain.