Interior Secretary James G. Watt yesterday received a vote of confidence from President Reagan as Democrats called for Watt's resignation or reprimand over a letter to Israeli Ambassador Moshe Arens.

"Does the president have full confidence in Watt? Does he in no way see Watt as a liability? The answer is yes," White House spokesman Larry Speakes said. Reagan has no plans to summon Watt to discuss the letter, which the White House continues to disavow as "unfortunate" and not representative of administration policy, Speakes said.

The strong endorsement came a day after Watt said in interviews that he is "proud" of the letter, which drew protests from Jewish leaders and calls from Democrats for Watt's resignation. The letter cautioned that American support for Israel could be jeopardized if "liberals of the Jewish community" oppose Watt's aggressive energy development program.

Sen. Daniel Patrick Moynihan (D-N.Y.) said he plans to introduce a resolution today calling on the Senate to denounce and repudiate Watt's letter as "unacceptable." The letter "unjustly and egregiously impugns the loyalty of American Jews and . . . indicates a profound misunderstanding of the reason the United States is committed to the survival of an independent and democratic Israel," the Moynihan resolution says.

Moynihan, one of 12 senators to vote against Watt's confirmation, was the first to call for his resignation following reports of the contents of the June 17 letter to Arens.

Former Vice President Walter F. Mondale also called for Watt's resignation in a fund-raising speech in Eau Claire, Wis. "He has offended the American sense of fairness," Mondale said, calling Watt "an embarrassment to the American people."

Also responding to the letter, Rep. Edward J. Markey (D-Mass.), an outspoken Watt critic, announced hearings to investigate Watt's implication in the letter that national security justifies his accelerated offshore oil drilling program. "Is he saying we should sweep away a generation's worth of environmental laws because of national security?" Markey said.

Watt said he wrote the letter following a social conversation with Arens about energy and other matters at a Bonds for Israel dinner last month. He said he did not regard it as threatening, as alleged by several Jewish leaders. The leaders also criticized Watt for seeking their support through a foreign ambassador.