Interior Secretary James G. Watt admitted yesterday that he had "made a mistake" in warning Israeli Ambassador Moshe Arens that American support for Israel could be jeopardized if American Jews oppose Watt's energy policies.

Watt, who earlier said he was "proud" of his letter to Arens, told a private gathering of officials of the Anti-Defamation League of B'nai B'rith in New York yesterday that he regretted writing it and that American Jews had "every right to be upset" about it, according to ADL leaders who attended the session.

ADL officials said they appreciated Watt's candor and accepted his apology. "He spoke with great sincerity and in good faith and we consider the matter closed," said Kenneth J. Bialkin, the group's national chairman.

Hours after the ADL meeting, President Reagan reaffirmed his confidence in Watt for the second time in three days. "He shouldn't be fired," Reagan said at his press conference when asked about Watt's remarks. Reagan earlier disavowed the letter as "unfortunate" and not representative of adminstration policy.

The rapprochement in New York and the firm endorsement in Washington last night followed several days of attacks on Watt, culminating in calls for his resignation because of the June 17 letter and a second letter to Democratic members of Congress. Both letters made statements that the White House termed inconsistent with administration policy.

Jewish leaders accused Watt of making "veiled threats" in the letter to Arens, and denounced him for appealing to a foreign ambassador for American Jewish support. The letter cautioned that America may be unable to remain "the strong protector and friend of Israel that we are and want to be" if Jewish liberals oppose Watt's aggressive energy development programs.

Prominent Democrats called for Watt's resignation and a group of Senate Democrats introduced a resolution denouncing the letter. While that controversy raged, Democratic congressmen attacked Watt over another letter, this one warning that the United States might have to go to war in the Middle East if Reagan's energy policies are not enacted. That letter was sent on July 21 to 29 House and Senate critics of Watt's offshore drilling program.

In his press conference, Reagan explained what Watt intended to say in the two letters. He said the message of the Arens letter was that the United States is vulnerable to another oil embargo because of its dependence on foreign energy sources. Under an embargo, "we wouldn't be much of an ally to our friends, and that would certainly include Israel," Reagan interpreted the letter as saying.

Reagan said the letter to the congressmen intended to ask: "Where would the western world be if someday our source of supply was purely there in the Persian Gulf and it was denied to us?" Reagan said Watt has since "expressed the wish that he had second thoughts" about the second letter.

Watt's meeting with the Anti-Defamation League was scheduled six weeks ago at his request, well before the Arens letter became public, according to ADL officials. Watt wanted to promote his controversial program to offer 1 billion acres of coastal waters for oil and gas development in the next five years, the leaders said.

After opening his remarks with an apology for the letter, Watt proceeded to tout the drilling program to "a very sympathetic audience" of about a dozen ADL leaders, Bialkin said. He added that several members of the group pointed out to Watt that Jews have long supported the cause of energy independence.

Watt is scheduled to dine this morning with several leaders of the American Jewish Committee to discuss energy development. He told the ADL that he is seeking the support of all interest groups for the development plans and is not singling out the Jewish community.