It has been a coutious courtship, this meeting between America's new President and Israel's new prime Minister - one of carefully chosen words and thoughtful smiles.

And however was the reserved attitude more apparent than at a State Department lucheon and a White House tea given yesterday in honor of Alza Begin, Prime Minister Menahem Begin's wife.

"It is like two lovers before their mariage." said Sonny Crane, President of the National Council of Jewish Women. "First we must meet each other and talk to each other. Then we will learn to love each other."

But the courtship has been slow gracious. There was the feeling at the lucheon that things would work out between the new government in Israel and Washington. No need to rush.

Traditionally conservative members of the Jewish community had a chance to meet Mrs. Begin, a tiny, animated woman, over a carefully chosen Kosher lunch, the first ever served at the State Department dining room. Many found her quietly impressive.

"Her life with Begin is something like a movie scenerio," said Crane. "She has lived close to his power and spent countless nights alone having sent him at night, not knowing if they would murder him now or later."

And now that his minority party is in power the stigma of his "terrosirt" past haunts him, said Crane.

"It is true that Begin has always been outspoken, with the office comes maturity," said Val Siberman, national vice chairman of the United Jewish Appeal. "He is like Carter, really, very grass roots."

And like Rosalynn Carter. Mrs Begin is very open and personale. And involved.

"She has a deep feeling for the costs of war," said Max Cleland, administration of the Veterans Administration. "She spoke of the casualities in her country and said that it is often people know, your sons, cousin. She has been touched."

Tough perphaps overshadowed by her dynamic husband, some who met her - including Rosalynn Carter - pointed out that Mrs. Begin has become very involved in the casualties of Israel's wars, the veterans and the children.

The lucheon, hosted by Mrs. Cyrus Vance, was given at the Senate Department, and included Bert Lance, director of the Office of management and Budget, Mrs. Simcha Dinitz, wife of the ambassador of Israel, Mr. and Mrs. Robert Strauss, special representative for trade negotiations, and Mr. and Mrs. Eli Wallach (Anne Jackson), appearing at the Kennedy Center in "Absent Friends."

Rosalynn Carter hosted a tea later in the afternoon. Most of the guests were involved in Jewish organizations, education child welfare or veterans affairs.

"I think the Jewish community is going to rally around this new regime." Silverman said. "We may be cautious, but we know that democracy has chosen Begin and we are confident that he will work for peace."