Faced with mounting Republican opposition, the White House has agreed to drop the nomination of Sam Zagoria to a GOP seat on the Federal Election Commission.

The Senate Rules Committee was scheduled to vote yesterday on Zagoria's nomination. The committee canceled its session, congressional sources said, after Frank Moore, the Carter administration's chief of liaison, met with Senate Minority leader Howard H. Baker Jr. (R-Tenn.) Thursday night and assured Baker that Zagoria would either withdraw or he withdrawn by the White House.

Some congressional Republican had opposed Zagoria for the FEC seat because they said President Carter had promised Baker and House Minority Leader John J. Rhodes (R-Ariz.) that the GOP nominee would be selected only after "full consulation" with party leaders.

Zagoria, a former administrative assistant to Sen. Clifford Case (R-N.J.) and now director of the labor-management relations service of the U.S. conference of mayors, was not one of the three names that Baker and Rhodes forwarded to the White House.

"The tragedy is that Sam Zagoria was a victim in all this," one Republican said yesterday. "He is a very decent, honorable man. But the president just broke his word to the Republican leaders about how a nominee would be selected."

Zagoria said yesterday that he had received no word about his nomination except for a phone call Thursday night that yesterday's hearing was canceled. It is expected that Zagoria would receive another job in the Carter administration.

Neither Moore nor his assistant handling the FEC nominations, Bob Thompson, could be reached for comment.

When Moore agreed Thursday night to withdraw Zagoria, the Republicans agreed not to prolong committee consideration of John McGarry, the nominee for the available Democratic seat on the FEC, congressional sources said.

McGarry, a special counsel to the House Administration Committee and friend of Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), has come under fire for failing to disclose fully certain financial dealings.

At a hearing on his nomination July 27, McGarry acknowledged that he failed to list certain income or gave vague information about its source on House financial disclosure statements for 1973 through 1976 that were required by his job.

"We still have certain questions we will ask Mr. McGarry," a Republican aide said yesterday, "and we expect him to answer them fully. But we will let McGarry rise or fall on his own merits now, and not try to obstruct or prolong anything."

The next session of the Senate Rules Committee is scheduled for Tuesday at which time McGarry is expected to return for more questioning.

The FEC polices presidential and congressional campaign finances and approves public funds for presidential candidates.

The commission is made up of three Democrats and three Republicans, appointed to staggered, six-year terms. While the fight over new nominees goes on, Republican William Springer and Democrat Neil Staebler are continuing to serve on the FEC although their terms expired April 30, 1977.

Republican opposed Zagoria immediately after he and McGarry were nominated last October. They charged that Carter had broken with Barker and Rhodes made on Feb. 23, 1977. Because of the uproar, the Senate failed to consider the nominations and they died at the end of the session.

Bakker and Rhodes content that Carter assured them again last Jan. 19, that the nominee for the Republican vacancy would be selected only from names suggested by the Republican leaders.

However, Sen. Dick Clark (D-Iowa), told the Rules Committee Wednesday that he checked with the White House on behalf of the committee and reported that President Carter didnot recall making any such commitment.

In April, President Carter renominated Zagoria and McGarry.

Baker, a member of the Rules Committee, said at hearings Thursday, "In simple terms, I believe the president has reneged on an agreement."