One month after voters modified the stringent property tax limitations, Prince George's County Executive Parris N. Glendening announced yesterday that he is seeking authority from the state legislature to impose new taxes on utilities and parking.

Glendening, in a midterm analysis delivered at an Upper Marlboro press conference, stopped short of proposing new taxes for county residents. But he said he will ask the county's General Assembly delegation to begin working toward passing state legislation that would allow the county to impose the new taxes if needed.

The announcement drew an immediate barb from a leader of the county's legislative delegation, who has often been at odds with Glendening. State Sen. Thomas V. Mike Miller Jr., the county's Senate delegation chairman, said he has not met with Glendening to discuss the county executive's legislative agenda, but he said extra taxes should not be necessary.

"I think the people of Prince George's County have done a very noble thing in voting to increase taxation for themselves in November," Miller said of the TRIM reform. "It's a little premature to talk about extra taxation."

The TRIM modification approved by voters Nov. 6 will raise $7.3 million in increased property tax revenues, Glendening said, an amount that will not allow the 1985-86 budget to keep pace with inflation.

The amendment to TRIM (Tax Reform Initiative by Marylanders, passed in 1978) will freeze the county tax rate at $2.40 per $100 of assessed valuation. Before the change, TRIM mandated a $144 million revenue cap from property taxes.

But in order to decrease the sizes of school classes, increase teachers' salaries, upgrade public safety facilities and continue efforts to attract development, Glendening said more money will be needed.

"The question is whether we want to go beyond those survival levels and generate new services," Glendening said.

According to figures compiled by Glendening's office, the county collects five different state-authorized taxes, including admissions and hotel taxes. In Montgomery County, 13 such taxes, including telephone and residential, parking and utility taxes are imposed and account for $43 million of that county's budget, he said.

"Now that TRIM has been modified, what we are looking for is, if you have a range of revenue sources which are used throughout the state, why not use them here ?" Glendening said.

He specifically ruled out a telephone tax.

An effort by the county to raise revenue by increasing personal property taxes was overruled by the Maryland Court of Appeals last February. The tax, assessed on business equipment, was challenged by businesses, and the court ruled that the county could not set different tax rates for real and personal property.

Paul Rodbell, legislative liaison for the county Chamber of Commerce, said that the business community is aware that it may be asked to foot possible new tax bills.

"We know something's going on," Rodbell said. "Our position has been that as a business community we are always willing to participate fairly in revenue creation ." But any new taxes considered to be unfair by businesses, he said, will be opposed.

Glendening also said that during the final two years of his current term he plans to place increased emphasis in upgrading roads and public transportation, addressing environmental issues and creating a county parking authority with the power to finance construction of parking facilities.

He also said he is committed to running for a second four-year term in 1986.