Executive director Morris J. Amitay of the American Israel Public Affairs Committee (AIPAC), whose home was bombed early yesterday, is the chief representative of one of Washington's most effective and visible lobbying organizations.

As the umbrella organization for domestic Jewish groups in support of Israel - often called "the Israeli lobby" - AIPAC is a power to be reckoned with at the White House, State and Defense Departments and on Capitol Hill. And Amitay, who became chief of the 23-year-old organization two years ago, is a well known figure in government circles.

A grass roots organization with 11,000 members who pay $35 each to belong. AIPAC's essential strength is the intense political involvement on the local level of many American Jews.

A computerized list of "key contacts" for every member of Congress, for example, tells AIPAC who to call or write whenever there is need to get a message quickly and effectively to a legislator. Word from back home, which may come from a congressman's close friend, campaign aide, physician ofleader of the local Jewish community - the sort of influential Jews who are often part of AIPAC's organization - is likely to have greater impact than any suggestion from a paid lobbyist in Washington.

Due to its nationwide organization, excellent Washington contacts and the strong motivation of its adherents here and in the field. AIPAC with a headquarters staff of 18 is often considered a more potent lobby than business firms and trade organizations with several hundred Washington staff members. Earlier this month the Wall Street Journal, in a front page study, said the pro Israeli lobby "may well be the most effective of the many pressure groups in Washington - variously admired or feared."

An AIPAC mailgram to its membership in early June - shortly after Menahem Begin's right-wing opposition party won the Israel election - played a role in mobilizing American Jewish opinion to support Begin, war the Carter administration of domestic concern and head off a potential crisis in Washington-Jerusalem reltions.

According to AIPAC officials, serveral thousand letters a week and telephone calls from influential Jewish leaders poured into the White House. Carter suddenly assigned his chief political aide, Hamilton Jordan, to take a hand in Middle East policy because of the domestic implications.

At Jordan's request, AIPAC furnished a list of 21 Carter administration actions and statements that it considered anti-Israel. Vice President Walter Mondale was assigned to assuage the concerns of the Jewish community by making a major restatement of Middle East policy June 17 - and AIPAC quickly provided the White House with a critique of that unsuccessful effort.

After the State Department issued a warning to Israel about Begin's Middle East policies on June 27, U.S. policy toward Israel flared into a controversial issue in public circles far beyond the ranks of those who usually follow the question in detail. With encouragement from AIPAC, key members of Congress and the Democratic National Committee as well as leaders of organized labor and other influential groups registered concern at the White House. Carter's response was a meeting July 6 with 53 American Jewish leaders to reassure them of his intention to keep a close alliance with Israel and to avoid a confrontation with Begin.

Amitay had been in Israel to see Begin, not in Washington for the July 6 meeting. He, as well as many executive board members of AIPAC, were among those briefed by Begin in New York last Friday about his talks with Carter.

While it supports the interests of Israel as it sees them and maintains contact with the Israel Embassy. AlPAC says that it does not take its instructions from the Israeli government. Embassy spokesmen say the same.

In some cases Washington observers believe AIPAC and the pro-Israeli American lobby have been more militant about U.S. policy toward the Middle East than the Israeli government and less tolerant of any deviation from Israeli interests.

AIPAC officials expressed gratitude yesterday that through "a miracle" Amitay's life and those of his wife and children were spared in the early morning bombing. Even if the bombers had succeeded, there is little likelihood that the political power of American Jews on matters effecting Israel would have been seriously impaired. AIPAC and the views which it represents are deeply entrenched in the American body politic.