At his first formal news conference in nearly six months, a relaxed and smiling President Reagan faced the White House press corps and the American people unencumbered by past rhetoric or campaign promises and secure in the knowledge that he will never have to stand for reelection again.

The result was a confident president who extended conciliatory words to the Soviet Union, showed respect for Congress and used unusually low-key language in discussing such issues as urban crime.

Technically, the nationally televised news conference that Reagan held last night, his first since July 22, was the last one of his first term. Politically, it was the first of a second term in which he is free from campaign pressures and can say what is on his mind.

Until last night, for instance, Reagan had always been guarded about acknowledging that a freeze on Social Security is likely to be a part of any new deficit-reduction plan, even though some aides have whispered that this may be necessary. But at his news conference Reagan blandly and deftly suggested that he might accept such a solution if it were handed to him as a "possible congressional mandate."

He displayed similar equanimity on the subject of verifying a nuclear arms agreement, a subject on which he has often inveighed against the Soviets. Last night, in making what has become a familiar plea for the reduction of nuclear arsenals, Reagan said that "absolute verification is impossible."

Nearly four years ago, in his first news conference as president, Reagan picked up the words of a reporter's question and accused the Soviets of lying and cheating. In subsequent speeches he described the Soviets as "the evil empire" and the "focus of evil."

Last night Reagan answered repeated questions about Soviet intentions in language that aides said was deliberately intended to be unprovocative.

In the past, when he had to watch his words, Reagan's news conferences were sometimes considered an ordeal by both the president and his aides. Last night, by contrast, he seemed to be enjoying himself.

Asked whether he was ready to announce the appointment of Energy Secretary Donald P. Hodel as the new secretary of the interior, Reagan gave a stage smile and said: "I ain't talking."

Asked whether he ever talked to Richard M. Nixon, a taboo subject during his first four years in office, Reagan readily acknowledged that Nixon, along with other former presidents, had been briefed on arms control. Then Reagan added that he had called Nixon just yesterday -- to wish him happy birthday. Nixon was 72.

Reagan's aides were similarly relaxed.

Before the news conference, the president for possibly the last time walked to the East Room with a trio of longtime top aides -- White House chief of staff James A. Baker III, deputy chief of staff Michael K. Deaver and counselor Edwin Meese III -- all of whom are leaving their present jobs. Baker and Meese are to move into Cabinet posts and Deaver, the president's closest aide, is leaving the administration to go into the public relations business.

When Reagan had finished and was out of earshot of the press, all three aides joined him and, almost in chorus, told him it was his "best ever" performance at a news conference.

White House spokesman Larry Speakes, making a similar point, said afterwards that he looked forward to regular news conferences in the second term and said another would be scheduled late in February. As Reagan left the East Room, ABC News' Sam Donaldson asked him whether he would be back next month.

"Probably," Reagan said with a smile.

The questions last night seemed to mirror Reagan's mood. For the most part they were friendly in tone and not confrontational.

Speakes said that Reagan, who had for the most part decided in advance whom he would recognize, used the questions to make points that he wanted to make. This was especially true in response to another question by Donaldson, who brought up the issue of a New York man who allegedly shot four youths when they demanded money from him on the subway. Donaldson asked Reagan what he thought of using deadly force to defend himself.

Reagan would not comment on that case, expressed sympathy for those who feel threatened by crime and said that "there is a breakdown of civilization if people start taking the law into their own hands." Then he said that an attitude toward stricter law enforcement and punishment had produced a decline in crime.

The president discussed the departure of longtime aides, specifically Deaver and Interior Secretary William P. Clark, in almost detached terms.

In the immediate aftermath of the election Reagan had responded to questions about staff changes by saying he "didn't want to break up a winning team." But when these words were put to him last night by the Chicago Tribune's Storer Rowley, Reagan replied that he had long known that Clark and Deaver wanted to leave.

He made it sound as though Clark, a longtime troubleshooter whom Reagan named to the California Supreme Court, had been in military service.

"Secretary Clark, at my behest, was in public life longer than I was because, between being governor of California and being president, I had a few years as a civilian," Reagan said. "He didn't."

As at other news conferences, Reagan made his share of verbal slip-ups last night. He repeated a familiar, and inaccurate, statement that cutting Social Security costs would have no impact on the federal deficit. He also referred to a defense budget "increase" when he meant "decrease."

But the difference last night was that Reagan, who on occasion has become flustered by such errors, was singularly untroubled by them.

As he faced the press at the beginning of his second four years in office, nothing seemed to bother him