Israeli Prime Minister Menachem Begin arrived here yesterday for a three-day visit that is intended to improve strained relations but that will take place under the cloud of vehement Israeli opposition to the proposed sale of sophisticated U.S. radar planes to Saudi Arabia.

Beginning today, Begin and President Reagan, who have not met before, will have at least two rounds of private discussions covering a wide-ranging agenda that will include exploring closer military cooperation and ways to deal with such Mideast problems as the Lebanon civil war and autonomy for the Palestinian inhabitants of Israeli-occupied territories.

But the issue likely to be affected most immediately by Begin's visit involves the administration's controversial plan to sell an $8.5 billion package of jet plane enhancements and airborne warning and control system planes, known as AWACS, to Saudi Arabia.

Israel, which contends that the sale would endanger its security, is openly hopeful that its supporters in Congress will block the deal.

Administration officials have sought to play down the potential for friction in the Israeli position, but the AWACS dispute seems certain to be a major factor in determining whether Begin and Reagan can mend the rift in relations between their governments during recent weeks.

Begin, who had antagonized Washington earlier with his air strikes against Iraq and Lebanon, faces the problem of gauging how outspoken he should be about the Saudi sale during his visit.

Administration officials clearly hope he will keep his views muted, but opponents of the sale in the Senate, where the vote on vetoing the Saudi deal is expected to be close, have warned that the administration is likely to win there if Begin leaves the impression that Israel is easing its opposition.

Despite these warnings, Israeli sources say privately that Begin, believing an all-out public attack would have the counterproductive effect of making him appear to be an ungracious guest, plans a relatively low-key approach.

Specifically, these sources said, he will not raise the subject during his public appearances in this country but will be prepared to state the reasons for Israel's opposition when the news media and other audiences ask him about the AWACS sale.

Yesterday, Begin spent the day largely closeted at Blair House with his aides in preparation for today's formal welcoming ceremony at the White House and his first meeting with Reagan. Begin was met at Andrews Air Force Base by Secretary of State Alexander M. Haig Jr. and made no statement before leaving by helicopter for downtown.

On his arrival at Blair House, he found a crowd of well-wishers carrying signs of greeting and singing Hebrew songs from behind security barricades on the other side of Pennsylvania Avenue. With a smiling Haig at his side, Begin crossed the street and spent several minutes chatting and shaking hands.