The State Department has chosen a St. Louis architectural firm to draw up plans for tearing down the unfinished U.S. Embassy building in Moscow and replacing it with a more secure structure.

The firm of Hellmuth, Obata and Kassabaum will start design work on two options: demolishing the thoroughly bugged building and putting up a new one on the same site, or putting up a new structure on a nearby site. The State Department favors demolition, but some lawmakers want to complete the unfinished structure and use it for housing.

U.S. officials agreed as far back as 1972 to let the Soviets supply the labor and materials for the foundations and shell of a new embassy complex. Work began in 1979 and was halted in August 1985 with the building about 65 percent complete. Technical counterintelligence teams found the structure riddled with bugs that normal X-rays could not detect, steel reinforcing rods apparently designed to serve as antennas, and a bewildering array of other spy elements, including a sophisticated power source that could last 100 years.

Trying to take all the bugs out, experts concluded, would only result in undermining the entire building.

The State Department is now seeking Moscow's approval to rebuild with American materials and labor. Officials say it will cost at least $270 million to rebuild on the existing site and as much as $350 million to finish the compromised building for unclassified purposes and put up an equally large "classified annex" nearby.

Meanwhile, it is costing the State Department about $1 million a month to maintain the unused new building and make adjustments for inflation in the rebuilding estimates. A senior State Department official assigned to the project said decentralization in Moscow also may pose difficulties in getting building and demolition permits and in acquiring a new site.

"We now have to deal with a lot more players in the Soviet Union," he said.

He said Hellmuth, Obata and Kassabaum will probably begin work next month and in 11 or 12 months submit a design for the "teardown and rebuild option," along with a less complete "schematic" for construction on a nearby site. The fee, still to be determined, will come from $3.8 million recently reprogrammed for the Moscow project.

"The new building will be much more secure than the previous one, both because the construction process will be more secure and because the building itself will incorporate many features we believe will add to the security of our operation," the official said. He said the details are classified.

Hellmuth, Obata and Kassabaum has ties with a Japanese construction firm, the Kajima Corp., which gave it a $22 million loan in July for expansion of overseas offices and which can convert the debt into a maximum of 35 percent of the U.S. firm's stock. But a spokeswoman for the firm, Dana Collins, and the State Department said Kajima will have no connection with the Moscow embassy project.

"We looked at it very carefully," the senior official said. "{The architectural firm} is still 100 percent American. And everything on the embassy project will be done by American citizens with security clearances."