The U.S. Chamber of Commerce tried yesterday to heal policy differences between its strong-willed chief executive officer and its equally-strong-willed board chairman that threatened to split one of business' most influential voices in Washington.

Supporters of both President Richard Lesher, a diehard believer in supply-side economics who fought President Reagan's tax increase bill even though a majority of his board supported it, and of Chairman Paul Thayer, who demanded a greater say in setting the organization's policies, claimed victory after yesterday's three-hour meeting of the chamber's board of directors.

In a brief statement, the chamber itself acknowledged the differences between the two men and said that the meeting resulted in "a more-clear-cut, definitive working relationship between the chairman and the president."

Thayer, the chairman of LTV Corp., was reported by friends to have been "very pleased with the outcome."

The official of another business-oriented lobbying group, upset at the way Lesher was pulling the chamber, called the result of today's meeting "a modest victory for Thayer." He said the board told Lesher that it and its chairman run the chamber, not the president.

But a supporter of Lesher in the chamber hierarchy insisted that the board ordered "no change in policy, no change in the authority of Dick Lesher.

"As far as I can see it was a clear-cut victory for Lesher," he said.

The differing interpretations of the chamber board's actions illustrate the depth of the split within the 260,000-member business group. One business lobbyist here described it as a battle between economic ideologues such as Lesher, who as president has been chief executive officer of the chamber for the past seven years, and the more-pragmatically-oriented business executives who make up its membership.

The differences came to a head this summer when Lesher led an attack against President Reagan's $98.3 billion tax increase, which Thayer and a majority of the board supported. Besides angering Thayer and other influential members of the board, Lesher's actions alienated the White House, according to business sources here.

Thayer complained to friends at the time that he was unable to get Lesher to listen to him on the question of whether the chamber should oppose the Reagan tax increase. Known for his dynamic rule of LTV, Thayer was said to have decided that the job of board chairman of the chamber involved more than ceremonial speechmaking and ribbon-cutting and to have insisted on a role in formulating policy.

As a result, he called yesterday's special board meeting about 10 days ago.

Although many business lobbyists here believed it would result in either Lesher or Thayer leaving the chamber, others said that Thayer was not out to get the chamber president fired. If Thayer did not get a more-clear-cut role in decision making, however, it was believed that he would have considered resigning before his term ends in six months.

According to sources familiar with what went on in the closed-door meeting in the chamber's Greek Revival headquarters across Lafayette Park from the White House, the board insisted that the president consult with the chairman on significant issues.

"That has not been happening. It will be happening in the future," the source said.