The Metropolitan Council of Governments announced yesterday an intensive two-month drive to broaden public awareness of what it says is the most urgent problem facing the metropolitan area - lack of adequate water reserves.

Harold L. Miller, COG board chairman, urged citizens to conserve water by checking faucets for leaks and by installing devices such as water saving showerheads and valves in toilet tanks. Miller, who is mayor of Falls Church, said he had done this in his own home and that the savings had been substantial.

In a related development, the COG board appropriated $12,000 yestereday for a joint project with the Army Corps of Engineers to seek out public opinion on the water problem.

"We are not talking about an abstract, hard-to-understand problem, or one which is off in the distant future somewhere," Miller said at a crowded press conference. "We are talking about a problem that is here and now and very real."

Miller said he hopes the publicity drive will generate ideas from citizens on how best to approach the problem. These suggestions are to be discussed at a "water summit conference" scheduled for June.

At the news conference, Col. G. K. Withers of the Corps of Engineers recited the list of proposals for long-range solutions to the water supply problem over which various private and public groups have been squabbling for years.

These include use of salt-free estuary water from the Potomac River below Little Falls, building large and small reservoirs further upstream and pumping water wrom wells. Currently, the only water project under construction in the region is the Bloomington Dam near Cumberland, Md., which is expected to start storing water in 1980.

The role of the corps in the water controversy came in for some criticism at the board meeting, which approved the $12,000 for the study project.

John F. Herrity, chairman of the Fairfax County Board of Supervisors, said the corps, which is required by law to provide the District's water supply, is both "the player and the umpire in this game."

"The corps is no objective outside agency in this matter and their studies should be judged in no other context," he added.

But Alexandria City Councilwoman Ellen Pickering said the District would receive no water at all if it were not for the corps because it would be used by the suburbs.

Water table levels were reported below normal in January and February by the U.S. geological survey, but in Maryland the levels climbed above normal by the end of March. The Virginia water table is still two feet below normal.

"Conditions as of today don't indicate the summer period will be worse than any other summer," Wayne Solley of the survey said.

The long range forecast from mid-April to mid-May calls for above normal temperatures and below normal rain.