Prince George's Country Executive Lawrence J. Hogan who promised voters last fall he would cut the county budget, announced yesterday that next year's budget will rise by about $15 million, or 3.5 percent.

Hogan defended the increase as the lowest rise in the country budget in recent years, and said that $15 million makes up only a third of the cost inflation has added to country services. Besides, Hogan said, "this is not really my budget. I came in halfway through the budget process."

The explanation wasn't good enough for leaders of the all-Democratic Country Council, who watched Hogan, a Republican, score Rhetorical points against former Democratic Executive Winfield M. Kelly Jr. time after time during last fall's campaign by saying that Kelly's promises to reduce budget increases were not enough.

"Hogan was playing demagogue, and he probably knew it," said council member Gerard T. McDonough. "This increase is no surprise. I can't believe that he was follish enough to believe the figures he had in the campaign."

During the race, Hogan said he had a study that showed how he could cut as much as $43 million from the budget, although he added he was not sure he could use the plan. Kelly, menawhile maintained that the budget could not be cut, but promised that he would hold next years increase to 4 percent.

Kelly held budget increases to under 6 percent on the average during his four-year term, according to Sam Wynkoop, who served as Kellh's budget aide.

"Hogan had the advantage of being a challenger who could make exaggerated claims," said council member Parris N. Glendening. "Since he took office, I have seen Hogan shift on at least a dozen things he said he would do. I think what he's facing now is the reality -- and the reality is that when you have a$450 million budget, the dollar amount is going to have to go up, even if the services are less."

"It's the best we can do under the circumstances," said Hogan of the budget, which will not be released to the council for another 10 days. "I'm going to adopt a lot of programs that are going to reduce our costs, but I can't do all that between Dec. 4 and March 10."

To reach a budget figure of about $448 million, Hogan is planning to cut 640 country jobs through attrition, and make deep cuts in many county departments.

Hogan met with School Superintendent Edward J. Feeney Monday to discuss the school budget, and sources said that Fenney was "deeply disturbed" afater Hogan told him he planned to make deep cuts in school salaries and health programs, among other areas.

County officials also have budgeted a fixed amount for employe cost-of-living raises even though negotiations have not yet been completed with nine county unions."We are just going to hold tight on that," Hogan said, "and we may have to negotiate for a long time to do it."

"We've made some very deep cuts in the departments," said Hogan's chief administrative officer, Ken Duncan, who called the budget increase "the lowest in modern times."

"We haven't included anything for the increase in salt and expenses of the public works department or other expenses like that," Duncan said.

The only departments to receive significant increases in next year's budget, Duncan said, were the police, fire and corrections departments.

Hogan said his budget-cutting was hampered by the loss of 450 federally funded job positions in the county government, which would cost $6.3 million to replace.

But the county will be helped next year by an increase in state aid that is expected to reach $10- $15 million, according to budget director Bob Duncan.

County officals and council members pointed out that most of the increase in state money was good for only one year, and that with added inflation, Hogan's second budget would be far harder to cut.

"This year will be tight," said Glendening."But next year will be the real disaster."

Hogan and other county officials said yesterday they were not prepared to release specific figures on program cuts or increases.

And Hogan said he was not yet sure whether county residents would get a tax cut next year beyond the effect of TRIM, the voter-approved limit on tax revenues that will reduce the tax rate automatically.

"That will depend on the amount of state aid that will come in and on some other things we're not sure about yet," Hogan said.