Katharine Graham handed over stewardship of The Washington Post yesterday to her son, Donald Edward Graham, challenging him to use his "young energy" in leading the newspaper "into a whole new era of progress" as its new publisher.

In a happy, emotional response, to a room full of several hundred Post employes, Donald Graham said: "Today, as in the rest of my life, my mother has given me everything but an easy act to follow."

And the 33-year-old Graham, representing the third generation of family ownership that began in 1933 with Eugene Meyer, his grandfather, also gave the first hint about his goals as new publisher.

The "most important thing... is what we put in front of the reader every day," he said.

As publisher, Graham will have overall responsibility for news and editorial viewpoints of The Post. He has been in charge of the business side as general manager for the past two years.

Yesterday's transition had been planned for three months, and Katharine Graham noted that the formal announcement had been made in Wednesday editions of the newspaper -- 24 hours ahead of schedule -- because of "last-minute leaks."

Katharine Graham, who is 61 years old, will remain as board chairman and chief executive officer of the Post Co., working "even more closely" with company President Mark Meagher on planning, acquisitions, "on the overall thrust of the company looking toward the future," she said.

In addition, she will continue to have ultimate responsibility for editorial quality throughout the diversified communications firm, which owns Newsweek magazine, newspapers in Trenton, N.J., and Everett, Wash., four television stations and other enterprises. "This will surely be a fulltime job." she said.

As to why she is stepping aside now, Katharine Graham said "the answer, in fact, is easy. It is because Don is ready and I am ready."

And, then she added: "Actually I suspect Don was ready before I was ready." In any event, she said she was relinquishing her post "with many mixed emotions."

Looking back over the three previous family occupants of the Post publisher's job -- Meyer, her husband Philip L. Graham and herself, she observed that her son "has one unique advantage in taking over the job... he has had time to be trained for it."

New York Times columnist James Reston, a long-time friend of the Grahams, emphasized the same point yesterday in assessing the transition at a major institution of the nation's capital.

"I wouldn't hesitate to say that Donald Graham will be the most distinguished publisher of his own generation in this century," said Reston in a telphone interview. "No one has been trained for it better or used the time of training so well," Reston added.

The unusual training to which Reston referred included a year and a half as a D.C. city policeman, after Graham came back to this country from a year of Army service in Vietnam, and several years of work as city reporter, advertising salesman, production supervisor and many other positions on the business and editorial staffs of The Post.

Katharine Graham recalled yesterday that she was eager for her son to join the business side after Vietnam, but that he had prevailed, "to become acquainted with the city, its people, and its problems," as a police officer.

"I think it says a lot about the relationship Don and I have had and will continue to have. We have views that are remarkably parallel in general. We have a number of differences in particular matters, and these have been resolved over the years with a large degree of independence preserved on both sides."

Donald Graham also served as Post sports editor for a year before joining management, and Reston, a former sports reporter himself, said that "every publisher should be a sports writer."

Sports editing "probably includes the two greatest loves of his life," Katharine Graham said of her son yesterday.

Both Donald Graham and Reston expressed their admiration of Katharine Graham's leadership at The Post.

"No long research for adjectives is needed to describe what she has done; the description is in the newspaper. It was a good newspaper than (in 1963); it's far better now, incontestably so. It was a good business then, and it is a much better one today," said her son, citing publication of the Pentagon papers, the uncovering of Watergate and the downfall of former President Nixon, an increase of circulation by 200,000 a day and 350,000 on Sundays in the face of declining newspaper readership generally, and 10 Pullitzer Prizes.

Reston said that Katharine Graham's decision to step down as publisher now "was a very wise move... publishers usually don't like to give up."

Since Philip Graham died in 1963, Reston said, Katharine Graham has "picked up the pieces and established and expanded The Post, in one of the greatest achievements of jornalism in this country... It's a great story, what Kay has done on her own under the most difficult circumstances."

Donald Graham said yesterday that distinguished public figures and major companies had urged her to sell The Post in 1963, but that she did not because the "newspaper that had been built by the wisdom of her father and the brilliance and drive of her husband meant too much to her."

Katharine Graham was publisher of the Post for two months short of 10 years. And yesterday she emphasized the tradition of her family, especially Eugene Meyer, her father.

Meyer purchased The Post at auction in 1933 and saved it by underwriting 20 years of deficits until its strength of today was guaranteed by the acquisition in 1954 of the Times-Herald, making The Post the only morning newspaper here.

"For all those years, he persevered in the face of discouragement, and he also did a critical, unexpected thing. Although he was a passionate Republican, he established an independent political identity for the paper," the outgoing Post publisher recalled yesterday.

"He somehow persuaded able people to come aboard what looked like a very rocky, unstable, small venture -- and he encouraged them to arrive at their own conclusions and to express them, even when these were at some variance with his own -- and even when their opinions added to his already mountainous problems," she said.

From the beginning, Meyer had insisted that The Post "shall not be the ally of any special interest, but shall be free and fair and wholesome in its outlook on public affairs and public men."

Meyer turned over the job of Post publisher to Philip Leslie Graham, Katharine Graham's husband, on Jan. 1, 1946. "Especially relevant today, although he (Meyer) was obviously a very strong, dominating personality, he stepped aside, made Phil publisher, and let him run the paper when Phil was 30 and had been only six months on the job," Katharine Graham said yesterday.

Under Philip Graham, The Post entered new fields -- acquiring broadcast properties for the first time, a 49 percent share of a Canadian newsprint company and Newsweek magazine. "He built up The Post itself, infusing it with quality, energy, driver, momentum, local strength, and national impact, and -- last but not least -- his own characteristics: irreverence, healthy skepticism, and gaiety," she said.

In the McCarthy era, she added, The Post "first distinguished itself editorially in an issue of national impact, and at a time when its economic foundation was relatively insecure to say the least. We were both boycotted and slandered by powerful organizations and voices."

Philip Graham aso was a participator and creator, fighting for D.C. home rule, southwest Washington redevelopment and a White House position representing city interests.He founded the Federal City Council, a group of local leaders, and was active in national politics.

Katharine Graham has concentrated on continuing such traditions since assuming the family leadership of the newspaper after Philip Graham's death in 1963. She was 46 at the time and, she recalled later, "unprepared," "nervous and uncertain."

Yesterday, as she spoke to editors and top business executives of what has become the dominant Washington newspaper -- on with a new worldwide reputation garnered under her tenure -- Katharine Graham said:

"My owns aims as publisher -- to speak to them for just a moment -- were to take the tremendous opportunity offered us in 1963, to take the foundation laid in both news and business and build on it. We had the will and we had the means."

In business, she said, "I think we are well on our way to my goal, which was to be as well-managed as the best... to foresee where we want to go and how we want to get there..." If elementary business objectives are met, "we can assure a decent return to our stockholders without a threat to the editorial independence and excellence on which we pride ourselves," she added.

Katharine Graham paid tribute yesterday to editors and business executives for "quite literally immeasurable" contributions since she gained controlling owner of the communications firm in 1963.

She cited the late Frederick S. Beebe, former board chairman, as "a guide and mentor to me and to all of us" from 1963 until his death in 1973, and credited former Post publisher (from 1961 to 1969) John Sweeterman with establishing a "successful and viable business operation" by paying attention to advertising and circulation growth, "the lifeblood of a newspaper."

In terms of circulation, The Post reported record daily sales of over 559,000 in the six months ended last Sept. 30, and record Sunday sales of more than 786,000. Advertising lines in the newspaper exceeded 90 million last year and accounted for more than 70 percent of Washington daily newspaper ads.

Revenues of the parent company are currently running at a level of a half-billion dollars a year, with profits in the first three quarters of 1978 up 31 percent, not counting nonrecurring gains.

In an interview prior to yesterday's transition, Donald Graham emphasized that The Post will continue to consider local news its top priority. "People in Washington basically have a strong desire to know the community where they live," he added.

Among his first challenges will be overseeing negotiations with the newspaper's labor unions, all of which have contracts expiring this year or, in the case of the Newspaper Guild, representing editorial and commercial employes, are seeking an agreement after nearly three years of bargaining.

Given strikes earlier in this decade, including a confrontation with pressmen after they damaged presses and subsequently were replaced in the wake of a bitter, three-month battle, it's "understandable" that "there's some concern on the parts of some members of those unions," he said.

"While some important issues are to be settled, we are ready to start talks early and negotiate quickly new contracts that we hope will show we intend this to be a good place to work," Graham stated.

Yesterday, he told The Post workers and officials: "I am young and relatively inexperienced, and I'm going to need your help.... what this group and the employes of The Post have been through together leaves us a feeling of shared loyalty and respect for each other, and a common understanding of our job."