President Carter, besieged by growing criticism of the energy shortage, announced yesterday that he is empowering the nation's governors to impose mandatory measures to regulate the distribution of gasoline in their states.

In what White House officials later conceded was a limited action, Carter empowered the governors to institute odd-even day gasoline rationing plans, to set minimum gasoline purchase requirements to discourage "topping off" of tanks and to regulate the hours service stations are to assure that some stations are open at all times.

The president's action directly affects 18 states whose governors currently lack authority to impose such regulatory measures in the event of more severe energy shortages. It leaves the decision on whether to impose the measures, which may never be put into effect, up to the governors.

[The White House said the governors of 19 states did not previously have such emergency powers, but Texas Gov. Bill Clements was granted that authority earlier this week, the Associated Press reported.]

White House officials acknowledged the limited nature of the action, which they stressed would not produce any more gasoline or substitute for mandatory conservation plans that Congress has rejected. But they said the action was one of the few Carter could take without congressional authorization.

The majority of the nation's governors have been given similar authority by their state legislatures, and the others could ask for it from their legislatures in an emergency. But with political pressure growing for some decisive action on gasoline supplies, the president moved unilaterally yesterday under what White House officials cited as his authority under the Emergency Petroleum Allocation Act of 1973.

Carter announced the action at a nationally televised news conference that was dominated by questions about energy and his deteriorating relations with the Democratic-controlled Congress.

On other topics during the news conference, the president:

Asserted that there has been "some harassment" of the families of five Soviet dissdents recently released from prison and "some delay" in obtaining the promised emigration of the families from the Soviet Union. But he said he did not know whether this was deliberate or the result of "the unwidely Soviet bureaucracy," and predicted that the families will be freed.

Said it would be "counterproductive" for the United States to present its own plan for Palestinian autonomy at the start of the West Bank and Gaza Strip talks between Egyptian and Israeli officials. According to diplomatic sources, the State Department, fearing further isolation of Egyptian President Anwar Sadat from other Arab leaders, has argued that early presentation of an American plan in the talks would tend to shore up Sadat. But White House officials rejected this argument, reportedly believing that it would be more effective to present a U.S. plan later, possibly after a deadlock between Egypt and Israel.

Said he has not made a decision on the deployment of a new mobile missile known as the MX, but called the weapon, now under development, a "stabilizing" factor in U.S. relations with the Soviet Union. "The most destablizing thing that we could have in our strategic relationship with the Soviets would be acknowledged inferiority or a vulnerable strategic deployment of missiles," he said.

Said he will decide by the middle of June whether to lift economic sanctions against Rhodesia. He said he would take into consideration the views of the new British government that the recent elections in Rhodesia were free and legitimate, a conclusion that could lead to the lifting of the sanctions.

The bulk of the news conference was devoted to domestic issues, particularly the growing deadlock between the White House and Congress over energy. Carter defended his policies, particularly his decision to order a gradual decontrol of domestic oil prices, said he intended to stick with his current position and professed unconcern over the political efforts of some Democrats to draft Sen. Edward M. Kennedy (D-Mass.) as the party's 1980 presidential nominee.

"I have not given up on any of these programs as far as getting them implemented by congressional action," Carter said when asked about several pieces of stalled administration legislation.

"But I will bear my share of responsibility if we fail," he continued. "My judgment is that the American people are beginning to feel that their own government can't deal adequately with crucial issues to the country, like inflation and like energy and like having a peaceful world in which to live. And until the American public gets aroused, we are going to have difficulty in Washington getting action taken. But I believe the public is becoming increasingly aroused as they see the need for this action."

Asked about Kennedy, the president grinned broadly and said he agreed with a recent statement by Democratic National Chairman John White condemning the effort to draft the Massachusetts senator. Carter added:

"No president can expect to have unanimous support even within one's own party. This has been the case with every predecessor of mine who lived in the White House. But that is not my major concern . . . If a few or even a large number of Democrats endorse someone else, that is their business. I will continue to try to serve the country as best I can and deal with the political question when the election comes along."

In defending his decision on decontrol of oil prices, which was over-whelmingly rejected in a nonbinding resolution adopted by House Democrats last week, Carter also appealed for an end to the increasingly harsh criticism that has come to mark relations between the White House and Capitol Hill.

"It is necessary to stop aggravating the problem by blaming one another and by seeking out scapegoats," he said.

Holding out on olive branch to Congress, the president rejected a suggestion from one questioner that he "punish" members of Congress who vote against him by withholding federal programs from their districts.

"I represent those districts also," he said.

Asked about inflation, Carter conceded that some recent major wage settlements have exceeded the adminstration's voluntary 7 percent annual wage guideline. But he said the problem was finding "a suitable alternative" and said he intends to "stick with" the program, even if it does not show quick results.

"In my opinion, a deliberate recession, which is one alternative, which would cause very high unemployment, is unacceptable," he said. "And mandatory wage and price controls, which have been tried in the past, and have never worked except during wartime, are also unacceptable. So we have a good, sound anti-inflation program. It is going to require some time for it to be effective, but I intend to stick with it."

Citing his concern about inflation, the president said he "doubts very serioulsy" that there will be a tax cut next year despite election-year pressures on him and Congress. CAPTION: Picture 1, PRESIDENT CARTER . . . defends his domestice policies; Picture 2, Carter: "No president can expect to have unanimous support" within his party. By Frank Johnston - The Washington Post; picture 3, President Carter peers over outstretched hands of reporters seeking recognition during question-and-answer session yesterday at White House news conference. AP