The Arlington County Board pledged continued financial support yesterday for Metro subway construction, but rejected a proposal that would have put the issue of how the county funds its share of the costs before voters this fall.

The board agreed to place four separate bond issues, totalling $12.4 million, on the Nov. 6 general election ballot.

County Board members, however, refused to support a proposal by Board Vice Chairman Walter H. Frankland that would have allowed Arlington voters to use bonds to pay the county's share of Metro's debts.

Frankland, who has been critical of Metro financing in the past, argued yesterday that the public should be allowed another say in transit spending, even though many officials say there is no requirement for such a vote.

Frankland said that when the first Arlington referendum was held in 1968, Metro's cost was projected at $2.5 billion. "Today the cost has quadrupled," he said. "We're at a juncture where it would be good to bring the issue back to the people."

His proposal died for lack of a second from any board member. Even so, the issue of Metro support is certain to be a key issue in the county's elections this fall.

Two board candidates, running with Democratic Party endorsement, are challenging Frankland's support for Metro, saying that neither the vice chairman nor his GOP-endorsed running mate, are as committed to the transit system as the Democrats are.

Frankland's referendum proposal would have allowed the county to issue up to $155 million in general obligation bonds to cover its share of Metro costs. County Manager W. Vernon Ford argued strongly against the proposal, saying, in a written report, that "the possible repercussions of a negative vote" on the bonds might kill plans for completing the full 101-mile subway system."

In related action, the board became the first area locality to promise its federal transit assistance funds to Metro to help pay off $1 billion of subway construction debts. The Department of Transportation announced last Thursday it would cut off federal aid to Metro in 1982 if the debt was not paid.

The County Board also approved a plan to continue construction of the 101-mile Metro system and to contribute $6.1 million toward the system's estimated price tag of $7.2 billion.

The financing plan covers projects for a three year period beginning in September and will include the purchase of rail cars and other start up costs as well as the construction of a second Potomac River crossing between the Pentagon and Gallery Lace in downtown Washington.

Members of the County Board also gave partial support to the Northern Virginia Transportation Commission, which wants to defer opening of the West Falls Church Metro station until early 1985. Residents of Falls Church had expressed fears that if the station is opened in 1984 while the rest of the line is under construction, the station would be a magnet for greatly increased traffic.

The Arlington County Board yesterday endorsed, in principle, the idea of deferring the station opening until the entire Vienna subway line is completed, but it asked that the matter be reconsidered in the future.

"I predict mounting interest on the part of Falls Church citizens to have it open when it's almost ready," said board member Ellen Bozman.

The largest bond proposal the board approved will be $4,665,000 for street and highway improvements. Other bonds to be voted on in November call for $1,985,000 for sewer construction, $1,705,000 for regional parks and $4 million for local parks.

The local parks bond provoked the only debate among the bond resolutions. The board heard from a dozen speakers, most of whom favored keeping a $7 million figure tentatively approved by the board last May. But the board voted 4 to 1 to cut that figure by $3 million.

Much of that $3 million had been earmarked for the purchase of part or all of three large undeveloped tracts of land -- Hendry, a 20-acre tract, at N. 24th Street on the Potomac Palisades; Gaddy, a six-acre tract on N. Stafford Street, a nd Freed, a 28-acre tract near Arlington Mill Drive and Walter Reed Drive. A 225-unit town house development is already planned for the Freed tract.

"I don't think the need has been shown for the purchase of any of these large tracts," said board member John Purdy. "It's one thing for talking about a few hundred thousand dollars . . . but the cost is too much."

Ken Ingram, a member of the Friends of Arlington Parks, was one who argued for maintaining the $7 million figure and purchasing the land. Said Ingram, "I'm extremely disappointed that the board seems to consider as a very low priority the purchase of the remaining open space in the county for its citizens."