Prime Minister James Callaghan flies to Washington next week, hoping to persuade President Carter to accord East-West relations a prominent place at the forthcoming economic summit.

Callaghan is expected to carefully avoid an overt criticism of what he regards as the President's interesting new initiative on human rights. But the prime minister is likely to urge some caution.

In a meeing with American correspondents today, Callaghan said that the "main theme" of his talks in Washington will be the "impact of the economic policies of the industrialized Western nations.' But he volunteered his belief that East-West relations will take up "a fair amount of time."

He is known to believe that the presidential attention drawn to abuses of human rights inside the Soviet world can be counter productive. It could, he thinks, raise expectations of citizens inside the Soviet bloc to dangerous levels, inspiring a mistaken belief that the West would support revolt.

Callaghan and his new foreign minister David Owen, 38, are due in Washington Wednesday evening for three days of talks with Carter and Secretary of State Cyrus R. Vance.

Callaghan's concern over the useful limits of the president's human-rights campaign appears at first glance to conflict with the strong endorsement Owen gave just last night. However, officials here today provided a gloss on Owens' speech that squares it with Callaghan's view.

Owen, it is said, shares Callaghan's misgivings. He is said to be particularly fearful that Carter's insistence on a theme touching so sensitive a Soviet nerve will endanger the principal fruits of detente. These, Owen said in his speech, were the U.S.-Soviet negotiations to limit strategic weapons.

The British view is that human rights and progress to reduce East-West tensions must not be linked formally. However, this argument runs, the Soviets will tie the two together.

In sum, Callaghan and Owen are likely to express in Washington a view not very different from that of former Secretary of State Henry A. Kissinger.

Callaghan evidently regards human rights and East-West relations as so critical that he wants Carter and the other five government chiefs to discuss the question at the economic summit meeting, tentatively set for London in May. France and West Germany have already evinced a coolness toward the human rights drive.

This time, Callaghas is known to be especially concerned about joblessness among youth which, in Britain as in the United States, is far above the national average.

Callaghan and Owen will discuss Rhodesia with their hosts but the British are not likely to propose any new initiative. Callaghan is known to believe that the United States has the muscle and Britain only some influence in southern Africa.

He thinks that South Africa is in the best position to persuade Rhodesia's white prime minister Ian Smith to make a deal with the country majority of blacks. Washington, unlike London, has clout in Johnnesburg.

He will also urge Carter to use his influence to persuade New York City to give the supersonic Concorde airliner landing rights. Callaghan's trip over in the plane will both advertise its speed and serve as an implicit warning that the strong relations will be hurt if the plane is barred.