The American public strongly endorses President Reagan's decision to keep a military presence in the Persian Gulf and supports the use of force to ensure an adequate supply of Middle Eastern oil, a Washington Post-ABC News poll indicates.

The five-day survey of 1,509 adults, completed Monday, shows a much closer division on Reagan's plan -- not yet implemented -- to provide U.S. flag status and U.S. military escorts for Kuwaiti tankers. There is significant public apprehension that the United States may have trouble coping with the military risks in the region.

The poll shows a spotty scorecard on the president's leadership -- with large and growing doubts about his candor in the Iran-contra affair, continued opposition to his policy in Nicaragua but sharply higher approval of his handling of relations with the Soviet Union.

Overall, Reagan gained a 52 to 47 percent approval measure -- well below his ratings before the Iran-contra affair was exposed last November but breaking into positive ground for the first time since January. However, his credibility on all the Iran-contra questions continues to erode as the televised congressional hearings unfold. Two-thirds of those questioned said they think Reagan will continue to have serious problems because of that controversy.

The poll also measured a sharp erosion of trust in Vice President Bush's account of the affair, with only 32 percent saying they believe he has been telling the truth -- down 13 points from a similar question in January.

The first Post-ABC News poll since the frigate USS Stark was struck by Iraqi missiles, with 37 sailors killed, showed no inclination by the public to pull back from the Persian Gulf.

Fully 75 percent of those interviewed said they agree with Reagan that the United States "should maintain a military presence in the Persian Gulf to protect our interests in the region." By 57 to 39 percent, they expressed support for the statement that the United States "should take all steps, including the use of force if necessary, to ensure an adequate supply of oil from the Middle East."

A similar question split the American public 45 to 44 percent in October 1981, and there were suggestions of hedging in some other findings in the new poll. The Reagan plan to put U.S. flags on some Kuwaiti oil tankers and provide them Navy escorts -- a proposal being questioned by many members of Congress -- was endorsed by a shaky 53 to 44 percent measure.

A 49 percent plurality said they thought other Navy ships faced a serious danger of attacks in the gulf, while only 46 percent expressed a great deal of confidence that such ships could defend themselves from attack.

Virtually all those surveyed -- 98 percent -- said they had heard about the Stark attack. Richard Wirthlin, who polls for the White House, noted that "Americans almost always rally around the president when our military forces are under attack, and that has been particularly true of this president." But Reagan gained only a 49 to 41 percent approval rating for his handling of the Stark incident, and overall approval of his handling of foreign affairs was at 39 percent, up only slightly from his all-time low of 33 percent in January.

Wirthlin said he was "a little surprised," therefore, that such a high percentage of those interviewed supported the U.S. military presence in the gulf. Past polls by other organizations, he noted, have sometimes shown less support for specific actions involving military risk than for broad foreign policy principles.

Reports of brightening prospects for a U.S.-Soviet arms agreement have brought the president strikingly strong ratings in that area of policy. The 62 percent approval of his handling of relations with the Soviet Union is 23 points above his overall foreign policy rating. A 67 percent majority said they think Reagan seriously wants to make progress in arms control and 51 percent have the same view about Soviet leader Mikhail Gorbachev.

This survey -- the first by The Post and ABC News since the start of the televised congressional hearings on the Iran-contra affair -- strongly suggests that this issue is a continuing problem for Reagan as well as a growing headache for Bush.

The percentage of those surveyed saying Reagan has told the truth about the Iran situation fell to 29 percent -- the lowest figure yet recorded. Only 34 percent said Reagan is doing as much as he can to bring out the facts -- another low point. And just 24 percent said they believed that Reagan had learned about the diversion of money to aid the contras only last November, as he has maintained, while 73 percent said they think he knew about it earlier. For the first time, a narrow majority -- 51 to 47 percent -- said they think Reagan participated in an organized attempt to cover up the facts about the Iran-contra affair.

Less than half of those surveyed -- 46 percent -- said they were following the congressional hearings very or somewhat closely. By 50 to 36 percent, they said the hearings have not tended to back up Reagan's statements about the affair, and they split evenly on the question of whether Reagan had broken the law on Iran or the contra funding.

Actions by administration officials in soliciting funds for the contras from other countries and from private citizens were disapproved of by overwhelming margins, with few people saying they thought the officials had the legal right to do what they did. About 42 percent said they thought the Iran-contra affair was more serious than Watergate, while 44 percent disagreed.

There was further bad news for the president on his fundamental policy toward Nicaragua. By 67 to 29 percent, those polled opposed further aid to the contras, and a higher percentage said the United States should not be involved in trying to overthrow Nicaragua's Sandinista government.Staff polling analyst Kenneth E. John contributed to this report.

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+ Q. President Reagan says a U.S. military presence in the Persian Gulf is necessary to protect our interest in the free flow of oil from that area. Do you agree or disagree that the U.S. should maintain a military presence in the Persian Gulf to protect our interests in the region? Agree 75% Disagree 24 No opinion 1 Q. How much confidence do you have in the U.S. military's ability to defend itself in such hostile territories as the Persian Gulf? Would you say you have a great deal of confidence, some confidence, very little confidence, or none at all? Great deal 46 Some 42 Very little 10 None at all 2 Q. Do you agree or disagree with the following statement: The United States should take all steps, including the use of force if necessary, to ensure an adequate supply of oil from the Middle East? Agree 57 Disagree 39 No opinion 4 Q. Do you think that other U.S. naval ships operating in the Persian Gulf are in serious danger of being attacked or was the attack on the USS Stark an isolated incident? Ships are in serious danger 49 Attack was an isolated incident 47 No opinion 4 Q. As you may know, the United States is planning to put the U.S. flag on some Kuwaiti oil tankers in the Persian Gulf and provide U.S. Navy escorts to help ensure adequate oil supplies for the U.S. and its allies. Would you approve or disapprove of U.S. ships escorting those oil tankers even if the U.S. ships risk being attacked? Approve 53 Disapprove 44 No opinion 3 Figures are from a Washington Post-ABC News telephone poll of 1,509 people May 28 to June 1.

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