Under strong White House pressure, congressmen whoonce called for a strict law to combat the Arab economic boycott of Israel have agreed to a weaker compromise bill, informed sources said yesterday.

Some unhappy Democrats said the comprocise was a retreat from President Carter's campaign promise to move vigorously against American firms that joined the Arab boycott of Israel.

The White House was apparently persuaded by State and Commerce Department officials that a tough bill would jeopardize trade relations with the Arab world.

Under White House-approved proposals to be submitted to the House International Relations Committee today, foreign subsidiaries of U.S. companies would be permitted to obey the boycott restrictions if they first obtained presidential permission.

The old bill, sponsored by Reps. Benjamin Rosentha 1(D-N.Y.) and Jonathan Bingham (D-N.Y.), would have barred any American company, or its overseas units, from obeying the boycott and the Arab blacklist of American firms.

Rosenthal, a leader of those pushing for strong legislation, played a key role in arranging the compromise. "He wanted to help the Carter administration avoid a major embarrassment on a very hot issue," said a source close to the congressman.

A White House source denied that the bill was being softened. The compromise "will be agreeable to all elemnts of the committee," the source said, and leaers on the boycott issue "are agreeable to what has been worked out."

Arab nations have a lengthy black-list of American companies they say have helped in the economic or military development of Israel.

American firms working on Middle East contracts are often called on to avoid using blacklisted firms as subcontractors or suppliers. Many members of Congress have attacked this system as foreign interference because Arab customers, in effect, told American firms to boycott other American companies.