Gov. Mario M. Cuomo is not a presidential candidate. He came to Washington this week and showed again why so many Democrats wish he were.

In welcoming a question about Israel, the New Yorker showed that, unlike other major Democrats, he has the stomach for huge moral problems and the courage to approach them in a political way.

Members of both parties, especially presidential candidates, flee from discussion of barbarities in the occupied territories. It seemed that a peak of horror was reached when Israeli soldiers, using a bulldozer, reportedly buried four Palestinians alive. At least they had come up with the perfect metaphor of the hard-line Israeli solution.

Maj. Gen. Amram Mitzna, commander of the West Bank Israeli forces said, "Even in my worst dreams I would never imagine such a thing."

But the horrors go on, and politicians are mute.

Cuomo came here to testify in behalf of a bill introduced by Sen. Edward M. Kennedy (D-Mass.) that would provide schooling and care for prekindergarten poor children. When he stepped out in the hall, he was surrounded by reporters who wanted to explore the presidential scene. One correspondent pressed him hard on the what-if question. Cuomo finally turned to her and said, "You know what? You're beautiful, but you're boring."

Did he have a comment on Israel? Other politicians regard any introduction of the topic as a hostile act. Cuomo, however, was not dismayed.

He is no stranger to this type of deadly civil disturbance or to the hatreds that underlie its ghastly excesses. He made his name in politics by refereeing a nasty housing fight in Forest Hills. More recently, he moved into the situation at Howard Beach. He talked to both sides, set the judicial processes in motion. Justice was done.

What makes him different is that he approaches the subject of Israel's problems on the West Bank and in Gaza as a political problem. The candidates will doubtless say, "easy for him; he's not one of us." But the fact is he doesn't mumble about "violence on both sides" with the throat-closing anxiety of those who dare not alienate a Jewish constituency or seek sanctuary in the history of Palestinian terrorism, another favored dodge. He has looked at the situation for openings, and openings is what politics is all about.

"It is not intractable," he said, noting the divisions within Israel, the split between Prime Minister Yitzhak Shamir and Foreign Minister Shimon Peres, the dissent on the Israeli home front, the division among American Jews.

"The terrible, terrible protest has worked," he said. "There is movement towards some device for breaking the impasse. They have to make a deal."

Cuomo pointed out the irony that has not occurred to many on Capitol Hill: the assumption that we should manage the affairs of Nicaragua but mustn't interfere with our ally and client, Israel. Democrats who tremblingly voted against President Reagan's request for more military aid for the Nicaraguan contras are struggling to escape being charged with "abandoning" them while not encouraging them to fight on. Lately, those lawmakers have been appalled by pictures of that war's victims, terrified children without arms and legs who cry in the miserable hospitals of Managua. They know the money can go astray, but they feel better because they have earmarked $14 million for the maimed children.

We self-righteously apply to Managua procrustean standards of proper "democratic" behavior. But when Israel does the indefensible, we turn away.

"If we can have that kind of concerted interest in Nicaragua, why not in the Middle East?" the governor asked. "All that time and energy could help."

The common element in the two situations is fear. Democrats fear the revenge of Reagan as much as they fear the Jewish lobby. Members of both parties would rather talk about Nicaragua.

Rep. Chester G. Atkins (D-Mass.) said, "It isn't just expediency, it's the fear of stirring up anti-Semitism. It's always out there."

Sen. Bill Bradley (D-N.J.), whom Democrats also yearn for as a candidate, referred vaguely at a press breakfast to the West Bank as "a demographic time-bomb" -- and said, "I think we should give Israel a chance to address the problem."

Kennedy, usually a lion of human rights, has not spoken out about a policy that has gone from shooting to beating and back to shooting again. The Palestinian death toll is at least 61. The injured are estimated in the hundreds.

Only Cuomo, so far, has seen that leaders must lead. Strong words from U.S. politicians could hearten dissenters here and in Israel and bring pressure on Shamir to say, at last, enough.