U.N. Ambassador Andrew Young was the center of another international row yesterday, this time with David Owen, the British foreign minister, ofer Rhodesia.

Young told a reporter he feared the British might "run out" on the tangled Rhodesian conflict "and leave us with 30 years of trouble the way they did in the Middle East."

Then he issued a statement explaining that opposition Conservative "pressures" might induce Britons "to wash their hands of the southern Africa problem." He compared this to the ending of the British mandate in Palestine in 1948.

Yesterday, Owen, who still insists that he likes and admires the free-speaking Young regretted the American's tendency to "sometimes shoot from the hip a bit." The Foreign secretary expressed his satisfaction with the fact that Young had at least withdrawn his formal statement. Young said, "I withdrew the statement because it added insult to an already unnecessary injury."

It was not clear here whether Young's climbdown some before of after the British ambassador in Washington, Peter Jay, called Secretary of State Cyrus Vance for a clarification. The call was made late Wednesday night. Jay not only reports to Owen but is also a close friend. He is son-in-law to Prime Minister James Callaghan.

Last night. American diplomats characterized the incident as "very unfortunate but not serious."

Both British and American officials say there is not rift between them on either tactics or strategy for handling the continuing Rhodesian crisis.

Both will neither endorse nor condemn the deal worked out in Salisbury last week between white Prime Minister Ian Smith and some black leaders. It promises heavily qualified black majority rule.

London and Washington, it is said here, hope to bring black guerilla leaders into some eventual agreement with those who signed the Smith pact. Both that the current U.N. Security Council debate on Rhodesia will end on a muted note that will not split the British and Americans from black African states.

Owen spent 4 1/2 hours in Washington Wednesday with Vance and President Carter, working out tactics and strategy. Yesterday, Owen said here:

"There is total unanimity of view as to the approach . . . There is total agreement between the president, Secretary of State Cy Vance and myself and the British government."

Reports from Africa have said that the Americans and British are divided, that London leans towards an embrace of the Smith deal and the United States. Rejects any guerrillas and their Patriptic Front. These stories are discounted here as mischievous designed to split a partnership walking gingerly on a diplomatic tightrope.

Owen discussed Young's crack and his Washington talks at a meeting of Callaghan's Cabinet yesterday morning. It is likely that Owen explained that Young has his domestic political imperatives just like British politiclans.

There has been strong Conservative Party pressure here on Owen to embrace the Smith deal. Several leading Conservatives have large financial interests in Rhodesia, many are concerned about the fate of the whites andmost regard the guerillas as tools of Moscow.

Both London and Washington fear that the Soviets might use the Security Council debate to encourage the introduction of a resolution flatly condemning the Salisbury agreement and demanding international action against it. That would force Britain and the United State to veto the resolution, splitting off from black African states.

The prospect of casting such a veto is thought to be a nightmare for Young. He is said to have made a large personal investment in improving U.S. relations with black Africa and his labors could be ruined by such an outcome.