Republican opposition to a Carter administration nominee to a GOP seat on the Federal Election Commission yesterday grew to include 125 of the 146 Republicans in the House.

The members, representing liberal and conservative elements of the party, yesterday signed a letter urging Senate Republicans to "make every effort" to block confirmation of Samuel D. Zagoria to the elections panel.

"To permit this appointment to go through would violate presidential-congressional understanding and intent of the law and would do great damage to our party," the letter said.

The action was the latest in a series of protests over the nomination that Senate Minority Leader Howard H. Baker (R-Tenn.) and House Minority Leader John J. Rhodes (R-Ariz.), have charged violates an agreement they made with President Carter last Feb. 23. Carter, the GOP leaders said, promised to fill the seat from a list of names submitted by the Republican Party leadership.

Carter, however, rejected three names forwarded by Rhodes, and Baker and nominated Zagoria, director of the U.S. Conference of Mayors' labor management relations service, Zagoria, a former administrative assistant to Sen. Clifford P. Case (R-N.J.), was suggested for the post by Case and four other liberal Republican senators.