U.S. Steel Corp. said yesterday it will file unfair trade complaints against eight countries on Dec. 19, the day President Reagan promised to have his program to cut steel imports in place.

The announcement of the impending trade complaints appeared to be an attempt by the nation's largest steel company to intensify pressure on the White House to get steel-importing nations to agree to cut sales in the United States.

So far, U.S. Trade Representative William E. Brock said yesterday, there has been little progress in concluding import restraint agreements with the five countries he targeted: South Korea, Japan, Brazil, Spain and Argentina.

Japan agreed last week "in a general sense" to cut its U.S. sales, "but we haven't fleshed that out too much," Brock added.

Nonetheless, Brock said he still has "the expectation" of coming close to the president's goal of reducing imports to 18 1/2 percent from their present level of 26 percent.

"We are satisfied with the progress made so far" by Brock's office, said U.S. Steel Chairman David M. Roderick. "However, should it become necessary, we are confident that the president will honor his commitment to stop trade abuse in steel by every legal means at his disposal."

Roderick said the company is holding off filing the trade complaints until Dec. 19 "only out of deference to the president's steel program."

The complaints are being filed against five Eastern-bloc nations -- Czechoslovakia, East Germany, Hungary, Poland and Romania -- as well as Austria, Venezuela and Sweden.

None of them a major supplier to the United States, but U.S. Steel said the complaints "cover imports which have a significant impact" on its product lines.

The complaints involve either illegal export subsidies or dumping of steel at prices below their fair market value.

The company cited decisions in past trade complaints that found high levels of dumping as well as illegal subsidies.

"We believe the cases we will file on Dec. 19 are just as strong, just as well documented, and we fully expect to have our allegations confirmed," Roderick said.

He said other companies will file new complaints against other importing nations.

One facet of the administration's steel policy has been to encourage American companies to file trade complaints against countries they believe are engaged in unfair trade practices. Administration officials have defended this policy vigorously against charges by exporting nations that it is protectionist.