Soviet leader Mikhail S. Gorbachev challenged President Reagan at their windup summit meeting over the wording of the final communique, and they were "going at it pretty heavy until the end," White House chief of staff Howard Baker revealed Thursday.

Talking with reporters on the president's plane as Reagan flew from Moscow to London, Baker also pronounced the U.S. delegation satisfied with the results of the summit, which concluded Wednesday.Baker said he had hoped the two sides could have gone further on arms control but added, "We came out just about where it was predicted we could come out. It would have been nice if we could have gone any further, but nobody expected us to go any further."

Asked why Reagan appeared so fatigued over the past couple days, Baker said, "We're all tired, I guess, but most of us are more tired than he is. I don't think that fatigue played any role in the summit.

"I'm sure he's tired and I guess he looks tired," Baker said of the president.

Baker described Gorbachev as a strong leader and said he demonstrated the same image in private as he did at his nearly two-hour news conference, where he was feisty and appeared entirely in command.

In talks with Reagan, Gorbachev "goes on at some length but he does not filibuster. He says what he says, and he doesn't back up and say, `I meant to say so and so,'" Baker recalled.

"He comes out of the box saying what he meant," Baker said.

Unlike earlier summits, Baker said that Reagan did not share with Gorbachev his store of jokes about life in the Soviet Union.

"He told him some lawyer jokes, and I didn't like that," joked Baker, an attorney.

Baker described the scene at the final Reagan-Gorbachev meeting on Wednesday morning, about six hours before the summit communique was released to the press.

"As the meeting ended, all of us stood up, including the president and the general secretary, and the president and general secretary continued to pursue their conversation.

"They were going at it pretty heavy and I was proud of the president. They were face to face and going at it pretty heavy until the end."

Baker explained that at the first meeting, on Sunday, Gorbachev had given Reagan some papers describing items that he wanted to discuss over the next three days.

Baker said the president gave it only a cursory look, and that Gorbachev quoted a phrase from the documents about "peaceful coexistence."

Reagan said something like, "that looks all right to me," and the documents were passed on for review by Secretary of State George P. Shultz and the staff of the National Security Council, Baker said.

Gorbachev's document would have put the two leaders on record as believing that "no problem in dispute can be resolved, nor should it be resolved, by military means. They regard peaceful coexistence as a universal principle of international relations.

"Equality of all states, non-interference in internal affairs and freedom of socio-political choice must be recognized as the inalienable and mandatory standards of international relations," the Soviet draft said.

At his Spaso House news conference in Moscow Wednesday, Reagan was asked why he took issue with the "peaceful coexistence" language.

Reagan said that he liked "the whole tone" of the draft language.

But the president also said that aides studying the draft communique "saw where there could have been certain ambiguities in there that would not achieve the general thought of what was being proposed."

U.S. officials were suspicious about the language, feeling it was too imprecise.

The U.S. objections were brought to the attention of the Soviets early on, and negotiations began at the staff level on alternative language, Baker said.

"And indeed, it was our impression that alternative language had been agreed to for the departure statement," he said. "And it was at the last meeting (that) the general secretary came back and made another run at trying to get his original language in. And the president held his ground."

"I don't think he (Gorbachev) was playing a trick. I think he was just making a run for his original formulation," Baker said.

In the end, the compromise language negotiated by the staff - omitting the words peaceful coexistence - was included in the communique.

Baker said the talks in Moscow were "more free-flowing" than in Washington and that there was "more energy in the conversations."

"They talk more freely. When they disagreed they would say so more quickly," he added.