The Alexandria City Council postponed indefinitely last night plans to buy the Old Dominion Boat Club's waterfront property because the U.S. Justice Department refuses to allow the 105-year-old club to build a new facility at another waterfront site.

The council has long wanted to buy the land at the foot of King Street occupied by the club's boathouse to open to the public the city's most centrally located waterfron site.

Mayor Charles E. Beatley has said a park on King Street would greatly enhance the multimillion-dollar development plans along the waterfront.

"This just about kills the plan," council member Donald C. Casey said last night. "Maybe some day the foot of King Street will be open to the public. But if the federal government isn't going to let the club move, what can we do?"

On March 26, the council tentatively approved a proposal to move the private club eight blocks north along the waterfront to a site the city would provide at the foot of Montgomery Street.

.The city also would have paid Old Dominion $1.5 million for the King Street site.

But before council members could vote final approval of the land swap last night, Harry P. Hart, the attorney for Old Dominion, told them that the Justice Department would not allow the club to build a new facility along the waterfront.

"I thought if the city okayed the plan the federal government would too," Hart said.

James Draude, a Justice Department lawyer, said in an interview last week that the federal government never planned to approve any such waterfront development in Alexandria.

"We want to keep as much of that land free from buildings as possible," he said, "and as long as we have title to the property we are going to do just that."

The Justice Department has claimed, since it filed a suit in 1973, that the 1 1/2-mile strip along Alexandria's waterfront consists of landfill owned by the U.S. government.

The suit, which is still pending, has proved expensive and frustrating for Old Dominion.

"I thought they the federal government would leave us alone if we moved," said Arthur King, 92, one of the club's oldest members. "But I don't know if this squabbling is ever going to stop."

Hart said that at least for now Old Dominion and its 550 members will continue to battle the federal government from its waterfront post at the foot of King Street.

"This has been going on for a long time, but we'll never give up hope," he said.

In other action, the council approved sale of $30 million in tax-exempt bonds for construction of a 324-unit apartment complex. The project, Park Center Phase II, will be built near the King Street-Shirley Highway interchange and is expected to be complete in 1987.

In order to qualify for the funds, the developer, Erkiletian Construction Corp., agreed to set aside 20 percent of its units for moderate-income tenants.

The rents for a one-bedroom apartment for such tenants will be $645 a month, compared with $795 for other tenants.