John Menke, a member and past president of the Montgomery County Council, announced yesterday he will seek the Democratic nomination for Montgomery County executive.

Menke, 37, is one of three Democrats who hopes to succeed James P. Gleason, the county's first executive and a Republican, who has said he will retire at the end of the year.

The three Democrats - Menke, Montgomery State Sen. Charles W. Gilchrist and Montgomery Planning Board Chairman Royce Hanson - are competing for the Democratic nomination in the Sept. 12 primary.

The race has become increasinly divisive for Montgomery Democrats as leading Democratic factions, hoping to coalesce aroung the strongest contender have failed to agree on anyone, thus broadening longstanding party rifts.

Although he acknowledged he is the underdog in the competition, Menke, a physicist, said he also is the only consensus candidate and the one Democrat who is electable to the office this year.

Menke said he is the most competent in the field as a four-year county council member who has the "experience and ability to jump right into the job next December."

Standing on the steps of the Rockville railroad station, Menke cited soaring costs of government, economic development, affordable housing and regional warfare" over water supply, sludge and sewerage disposal as pressing problems facing the next executive.

"I know the job already," said Menke. "I know who the good people are in county government, and I know who the duds are. I know where the management is lax and how to simplify and reorganize the county government."

Menke also called for upgrading existing roads rather than building new high-speed freeways, completing the 100-mile proposed Metrorail system, "cost-effective" energy conservation in county government and improved relationships between the Montgomery executive and the county school board.

Menke was elected to the council in 1974 after leading community opposition against the expansion of proposed sewage treatment facilities and a power plant at Dickerson near his Barnesville neighborhood.

He served as county vice president in 1975-76 and president in 1976. Menke is chairman of the council's environmental matters committee and has been a member of the Metropolitan Washington Council of Government's air quality planning committee and water resources planning board.