The Reagan administration said yesterday that the trigger prices for most steel products will remain unchanged for the fourth quarter despite cries for higher price levels from some steel industry factions.

The Commerce Department said trigger levels for October through December will remain at third-quarter levels for integrated steel producers, that is, firms that begin with the raw ore and manufacture a finished product. Trigger prices are based on the most efficient steel producer -- the Japanese. Because Japan's production costs didn't change during the third quarter, the Commerce Department said it didn't alter trigger-price levels for the domestic industry.

If prices of imports go below the trigger prices, the government initiates an investigation.

"The American Iron and Steel Institute considers it unfortunate that trigger prices for imported steel mill products . . . will remain unchanged from the third quarter," said William J. De Lancey, chairman of Republic Steel Corp and chairman of the industry group. "Continuation of unchanged TPM price levels for the second successive quarter fails to reflect Japanese steel-making cost increases monitored by the institute from public sources."

Meanwhile, foreign steel producers had been pressing for lower steel trigger-price levels, saying they are at a disadvantage because a strong dollar makes their products cheaper and because domestic producers must pay higher interest costs.

Commerce said there will be small declines in trigger prices for several products, particularly those made by electric furnace firms.