Former Alexandria mayor Charles E. Beatley Jr.said yesterday that he will not challenge Rep. Stan Parris (R-Va.) this fall, dashing the hopes of many Northern Virginia Democrats who viewed Beatley as their strongest candidate to unseat Parris this year.

Beatley, who was defeated by James P. Moran Jr. in a bruising campaign for mayor last May, said he decided not to run because Parris has such a formidable fund-raising operation. By the end of 1985, the Republican had raised $231,643.

"I'd have to play catch-up at this point," said Beatley, a retired airline pilot.

Beatley, who dominated Alexandria politics during his 15 years as mayor, revealed his decision at a meeting of the 8th District Democratic Party Wednesday night.

Fairfax Democratic Party Chairman Harris Miller said that a number of people have told him they may be interested in running. None of them has previously held office and or are well known in the district, which includes Alexandria, southern Fairfax County and portions of Prince William and Stafford counties.

That may make the fall elections in Virginia's 8th Congressional District a stark contrast to those of the past decade of politics. The district's rapid growth has made it one of the most volatile areas in the state. Most recent congressional races have been close, and Parris often has made the list of vulnerable House members from Virginia.

Miller said that some Democrats may be waiting until 1988. Parris has indicated he is restless in the House and may retire after his next term, possibly to run for governor. Last year Parris made an unsuccessful bid for the Republican nomination for governor.

"There may be some who think that rather than take on an incumbent, they would rather wait until 1988 when there is a vacant seat," Miller said.