President Carter's new task force of local, state, and federal government officials dealing with water policy convened for the first time yesterday and decided to focus its attention on three controversial questions about the quantity and quality of public water supplies.

In a four-hour meeting at the White House, the task force members agreed to concentrate on federal-state sharing of the cost of water-projects, funding, in advance, of the complete cost of new projects (as opposed to year-by-year appropriations), and federal aid for repairing aging water and sewer systems in major cities.

All three areas have been points of contention among Congress, the Carter administration, environmentalists and local governments in the continuing debate over Carter's national water policy.

After sparring with Congress for most of his first year in office over federal water spending, Carter last June enunciated what he called the nation's first comprehensive policy statement to govern the 25 federal agencies that spend about $10 billion in federal funds on water projects of one sort or another.

At the urging of the National Governors' Association, the president then set up the "Intergovernmental Task Force on Water Policy" to provide what is known in government circles as "input" from state and local officials to the federal agencies.

It was this group that held its first meeting yesterday. Among the 18 members present were Interior Secretary Cecil D. Andrus and Agriculture Secretary Bob Bergland, Lt. Gen. J.W. Morris, chief of the Army Corps of Engineers, the federal government's dam builders, Govs. George Busbee of Georgia and Scott Matheson of Utah, Mayors Edward Koch of New York City and Ted Wilson of Salt Lake City, and Neil Potter, a Montgomery County, Md., councilman.

In deciding to focus on federal aid to maintenance of big-city water systems, the task force yesterday sided with critics of Carter's policy statement. Local officials, particularly in the East, had complained about the statement's failure even to mention the problems posed by rusting, leaking water and sewage facilities in older cities.

Currently, there is no federal aid program specifically targeted at urban water system repair, although cities can get federal grants for such work from various programs designed to combat other urban problems.

The task force decided yesterday to have a subcommittee look into the need for specific federal programs in this areas. Such a proposal could spark a tough regional battle in Congress, because federal dollars sent to eastern cities would presumably reduce the funds available for major reclamation and irrigation projects in the West.

The task force's determination to study the "cost sharing" principle will put the group smack in the middle of one of the hottest water controversies: whether state governments should help pay for major water projects, which have traditionally been fully federally funded.

The group's third area of concentration, "advance funding," sparked the only significant disagreement yesterday between local and federal representatives on the task force.

The local officials want Congress to agree to appropriate, in advance, the full cost of local water projects. Under current policy, Congress appropriates such funds on a yearly basis, so that complete funding for any new project is never certain.

But federal representatives, noting that Congress this year rejected Carter's "advance funding" proposal, said they were reluctant to fight the battle again next year.