President Reagan embarked today on a week-long vacation that appears to have equaled the record for travel outside of Washington during the first two years of a presidential term.

By the time Reagan returns to Washington Sunday, after a week spent mostly at Palm Springs, he will have logged 53 trips and 175 days away from the nation's capital in slightly less than two years.

According to informal calculations, President Nixon logged an almost identical number of days outside of Washington in 1969 and 1970. The travel totals for Reagan and Nixon are far more than those of any other modern president.

Of the Reagan total, about 125 days were for trips that, like this one, are mostly vacation. The remaining 50 days were for foreign travel, including 10 days on a European trip in June and five days on a Latin American trip earlier this month, and for policy speeches and political campaigning.

The travel included 19 one-day trips in which Reagan returned to the White House residence at night.

The tabulations do not include days spent at Camp David, a favorite weekend retreat of many presidents.

Though Reagan has not traveled abroad as much as his four predecessors did in their first two years in office, his total time away from the White House is far more than that of any recent president except Nixon. Carter, for instance, spent less than 100 days away from Washington during his first two years in office.

The "vacation" calculation is not exact because presidents customarily schedule some newsmaking event on any trip. On Tuesday, Reagan is to recommission the battleship New Jersey in Long Beach harbor and use the occasion to make a defense speech before flying to Palm Springs.

One of the reasons that it is difficult to calculate the vacation time of presidents precisely is that their press secetaries usually maintain that the chief executive is working even when he is away from Washington on vacation.

White House spokesman Larry Speakes engaged in no such subterfuge today. Despite the appearance in Long Beach, Speakes said matter of factly the Reagans are on vacation and are not "trying to make news."

The stopover here was for the sole purpose of visiting Nancy Reagan's mother, Edith Davis, who has been in ill health for many years. Her husband, well-known surgeon Loyal Davis, died Aug. 19.

Reagan's latest vacation follows an inconclusive lame-duck session of Congress that White House officials have portrayed as a success.

But the White House staff has few illusions about legislative prospects in 1983, when Democrats will have more House seats and when GOP members of Congress are expected to be increasingly restive about economic and defense issues.

Speakes dismissed as an "untrue rumor" another published account, this one in The Washington Times, about a prospective staff and Cabinet shakeup. The report, labeled as rumor by the newspaper, said that Defense Secretary Caspar W. Weinberger would resign and be replaced by Sen. John G. Tower (R-Tex.).

According to the scenario, lame-duck Texas Gov. Bill Clements then would appoint White House chief of staff James A. Baker III to the Senate, Baker would be replaced by national security affairs adviser William P. Clark, and Thomas Reed, an NSC consultant, would take Clark's place.