The Reagan administration yesterday raised steel trigger prices 4.4 percent for the second quarter, apparently satisfying the nation's steel industry.

The Carter administration's failure to raise the second-quarter steel trigger prices a year ago led to the filing of a dumping complaint against steelmakers in seven European countries by U.S. Steel Corp. and increased tensions in the world trade arena.

The complaint was dropped last fall after the Carter administration devised a multifaceted plan to aid the steel industry.

The steel trigger prices are used to monitor steel imports that are sold here at prices below certain levels. The prices are based on costs of labor and materials in Japan, the world's most efficient steel producer. The government is supposed to intiate an investigation if imports enter below the trigger prices.

Republic Steel Corp. Chairman William J. De Lancey, who also represents the American Iron and Steel Institute, said yesterday, "We are encouraged by the evident effort which has been made by the Commerce Department to bring trigger prices closer to the Japanese costs as we believe them to be.

"In the first quarter, trigger prices were increased only 0.9 percent, which was far below the net cost increases which we believe had been incurred by the Japanese industry," De Lancey said.