Army Secretary Clifford L. Alexander Jr., overruling strong environmental objections, yesterday gave tentative approval for the long-delayed construction of the largest oil refinery on the East Coast in southeastern Virginia.

But Alexander said he is delaying a final decision on the $660 million project until he hears the personal views of Interior Secretary Cecil B. Andrus. The Interior Department has opposed the refinery planned at Portsmouth, Va., on the grounds it increases chances of oil spills in the Chesapeake Bay area and poses a serious threat to marine life there.

The Army secretary said he, not Andrus, will make the final decision on the permit and said he feels the economic benefits of the refinery far outweighed potential environmental risks.

Although it is preliminary, Alexander's approval appears to be both a crucial step forward for the project -- the first major refinery to be built on the East Coast since 1957 -- and another indication that the Carter administration plans to stress national energy needs over environmental goals.

As expected, supporters hailed and opponents deplored Alexander's support for the project, which has been on the drawing board for 10 years and has been a source of endless controversy among federal agencies. Virginia politicians, labor, business and environmental interests and Tidewater residents.

"It's a major breakthrough not just for my project but for all big plants," said John K. Evans, president of Hampton Roads Energy Co., the refinery's builder. "The administration has made a sound judgment on a cost-benefit basis."

"We have waited a long time for this day and I'm pleased and delighted," said Portsmouth Mayor Richard J. Davis, whose city stands to gain nearly $4 million in annual property taxes and 500 full-time jobs once the project is built.

Gov. John N. Dalton also hailed the approval, but cited the refinery as "a prime example of the costly delays and policy frustrations caused by over-regulation of energy development . . . [the] developers have spent more than $8 million to clear all the regulatory hurdles thrown in their path by the federal government."

One of the project's main opponents, Joanne Berkley of the Tidewater-based Citizens Against Refinery Effects, said she too was frustrated by what seemed to be yet another delay.

"His [Alexander's] decision, or lack of one, seems aimed at teasing everyone and putting additional pressure on Secretary Andrus," said Berkley. "There already have been too many delays and this is just another one."

The citizens group already is in U.S. District Court in Richmond challenging water pollution permits granted to the project by the state. Spokesmen for several environmental groups said yesterday they are considering lawsuits against Alexander if he gives the project final approval.

"The Chesapeake Bay is the largest estuary on the north Atlantic coast and they're selling it down the road," said Peter Holmes of the Natural Resources Defense Council in Washington, one of the groups."It makes a mockery of any sort of pretense of rational energy or environmental policy."

The project has been under study since 1969, when Hampton Roads Energy Co. first announced it was interested in building a refinery. When the Portsmouth City Council approved the refinery in 1975, its projected cost was $350 million.

The cost has nearly doubled since then, while federal and state regulatory agencies have been scrutinizing the project and taking positions. The departments of Energy, Defense, Labor and the Treasury favor the project largely because they say they see a need for more refining capacity on the East Cost, which now gets 49 percent of its refined oil from the Gulf Coast, 28 percent from overseas and only 23 percent from East Coast refineries.

The Interior Department and Environmental Protection Agency have opposed the project because of the danger to oysters and crabs, the potential threat to the bay's multimillion dollar seafood industry and the added air pollution the refinery would add to the area, which already violates many federal air quality standards.

Army approval is necessary because part of the 623-acre refinery and port facility would affect navigable waters under the Army Corps of Engineers regulatory control. The company submitted a permit application to the Army in March 1975.

Alexander had planned to announce a decision by Aug. 1 but said the added delay was 'because the issues are so sensitive and the environmental concerns so great."

In the end, he said, he was convinced the East Coast needs another refinery, that the Portsmouth location is as good as or better than 17 sites the Army evaluated, and that a major spill that could permanently devastate bay marine life is highly unlikely.

He noted that the refinery would process up to 250,000 barrels of crude oil daily and would have a storage capacity of 12 million barrels. The United States consumes about 18.6 million barrels of oil a day, according to most recent federal and industry estimates.

Alexander said his planned consultation with Andrus is required by a 1967 policy agreement between the two agencies. Interior Department spokesman Harmon Kallman said a meeting between the two secretaries may be arranged as early as next week.

"We're on record as opposed to the project and as of now our position remains unchanged," said Kallman. He noted that the agency considers the Hampton site "a very, very bad location -- one of the worst in the United States."

Refinery developer Evans said he does not believe Alexander's approval will end the controversy.

"There will be lawsuits flying back and forth for quite a while," said Evans. "Their [environmentalists] whole format is to delay and delay until we give up. Well, we're tough and we won't give up."