In its last days, the Carter administration turned down an appeal from the American steel industry for a special tax credit worth several hundred million dollars to speed construction of a modern, energy-saving production technique called continuous casting.

The Treasury Department informed the American Iron and Steel Institute that continuous casters did not qualify for the special 10 percent tax credit available for energy-saving installations, according to the guidelines established by Congress. Continuous casters -- like other capital investments -- are already eligible for the 10 percent investment tax credit and an approval of the AISI's request would have doubled the tax savings for the steel companies that installed casters.

There was no word whether AISI will ask the Reagan administration to reverse the decision by former Treasury Secretary G. William Miller.

There is no question that the American steel industry needs to accelerate the use of continuous casting to close a technology gap between itself and steel producers in Japan and other countries.

The process converts molten steel directly into solid, semi-finsihed shapes ready for processing into steel plate, beams, pipes and other products, eliminating several major steps in steel production. The technique produces higher-quality steel with fewer environmental problems, and at a lower cost.

"The most important technological change for integrated steelmakers during the next 10 years will be greater adoption of continuous casting," noted the Congressional Office of Technology Assessment in a 1980 study.

In 1978, more than 50 percent of steelmaking in Japan employed continuous casting techniques, while the level in the United States was only 15 percent, and among Amercan companies, the large steel firms trailed far behind smaller, specialized producers in use of continuous casting.

AISI contended that investments in continuous casting should qualify for the energy tax credit established by Congress in 1978 because of the vast amounts of energy saved by the more efficient process.

But Treasury officials said Congress intended the tax breaks to go only to to projects whose main purpose was conservation of oil or natural gas, in order to reduce U.S. dependence on foreign petroleum products. Energy conservation is only one of the reasons for investing in continuous casting, Treasury said, and the energy saved in the process often is coal, not oil or gas.

The industry is welcome to try again with the Reagan administration, a Treasury aide, said."I suspect it's going to be extremely difficult for them, however," the aide said.