West German political leaders are gradually being drawn into debate over an issue that most would probably rather not face.

The question they face is whether to extend once again the 30-year statute of limitations on prosecuting Nazi war criminals or to let that law take its course, allow the legal books to close and try to put one of the last and most visible reminders of the Hitler era behind them.

The current statute does not expire until Dec. 31, 1979, but the West German parliament will have to act in the months ahead if there is to be an extension. The debate certain to be bitter and emotionally bruising, has already started. It is a debate that jumps across party lines and splits politicians who might ordinarily agree with each other on more routine matters.

On one side are those who argue that, 33 years after the end of the war, it is time for West Germany to stop flailing itself with trials that dredge up the horrors of the past, that are exploitable by Bonn's current enemies, and that are increasingly hard to decide because witnesses and memories are old.

On the other side are those who say that Germany can never shut the books on war crimes trials or what federal Justice Minister Hans-Jochen Vogel earlier this week called "this terrible inheritance."

Vogel, in a personal statement of his views became the first member of Chancellor Helmut Schmidt's Cabinet to endorse publicly the idea of extending or completely doing away with the statute of limitation on questions of murder, so that the uncovering and prosecuting of additional major war criminals charged with murder could continue.

Yet, the West German political figures who enjoys the greatest reputation around the world as a liberal civil libertarian and so-called "good German" - former chancellor Willy Brandt - says he has not yet made up his mind on the very complex issue of whether to extend the statute.

In an interview a few weeks ago, Brandt said, "I would have to be convinced that we have to change the law," and his aides said this week that he still remains undecided.

"The large majority of our people rightly want a clean break with the past," Brandt said. He cautioned, however, that "a clean break cannot be a case of letting bygones by bygones. You cannot behave as if nothing happened."

What Brandt and others fear is that if the statute is allowed to just run out, then many Nazi war criminals whose whereabouts have never been uncovered may surface with no way to prosecute them or to protect West Germany from considerable embarrassment.

Brandt suggests that if the statute is not extended, the West German legal authorities should request all information from other countries on possible war criminals so that legal proceedings at least can be started in absentia before the law expires.

There are some 4,700 West Germans either awaiting sentencing or under investigation for war crimes by federal authorities. Even if the statute does run out, the law provides that these cases can be continued through trials if the investigation started prior to he statute's expiration.

Since the end of the war, West Germany's Central Office for Investigation of National Socialist (Nazi) Crimes has investigated almost 83,000 cases. Only about 6,500 have been convicted, however, and most of these were in the first 15 years of the post-war era.

Since then, conviction rates have dropped from about 10 to 2 percent as witnesses get harder to find and trials drag on for years and defense lawyers become more clever. In the veiw of some critics, the Germans have alos lost whatever drive they once may have had to prosecute them. Others, however, maintain that the West German courts are acting properly and democratically.

This week, the parliamentary floor leader for West Germany's Free Democratic Party, Wolfgang Mischnick, came out in opposition to any effort to extend the statue of limitations. Mischnick's party is the vital junior partner to Schmidt's Social Democrats in the ruling coalition in Bonn, so his statement -- in contrast to Vogel's -- provides initial evidence of how the issue is splitting political lines.

It is even splitting family lines since Vogel's brother, Bernhard, the Christian Democratic governor of the state of Rhineland-Palatinate, also opposes abolition of the statute.

Mischnick claims that extension or abolition of the statue could cause an upheaval in the West German judiciary, overburderning it with cases that, in the end, could not be solved. Difficulties in assessing evidence from witnesses could lead to unpopular acquittals, he argued.

Christian Democratic parliamentarian Benno Erhard also has come out in opposition to extending the law, claiming the statute itself was not an institution for overcoming the past and that West Germany should settle the question on German grounds and not be pressured from abroad.

There is, in fact, considerable pressure from some groups in other countries - including France, Israel and Poland - to extend the statute. Foreign Minister Hans-Dietrich Genscher reportedly has cautioned the Cabinet not to underestimate such pressures.

The original suggestion to extend the statute so there would be no time by the powerful, 72-year-old floor leader of the Social Democrats in parliament, Herbert Wehner, during a recent trip to Israel.

Wehner acted after Franz-Josef Strauss, the conservative leader of Bavaria's Christian Social Union Party, and historian Golo Mann, son of the author Thomas Mann, both issued a call for a general amnesty for crimes committed during the Nazi era. These proposals were careful to exclude from such an amnesty any crimes involving the murder of Jews, concentration camp atrocities or mass murders.

Mann argued that at this point the digging up of information about how people behaved in the Nazi era weakened the confidence of the West Germans in their country and leaders. He spoke not long after a popular state governor was driven from office after charges of wrongdoing as a Nazi military judge surfaced.

Strauss charged that "character assassination" so long after events was a favorite tactic of the Nazis and was used "to perpetuate the division of our people."

Brandt, Wehner and many moderate conservative leaders have sharply rejected any such general amnesty. "To absolve ourselves, by whatever kind of formal act, towards all others who have suffered injustice at the hand of Nazi Germany would not be good for us," Brandt said.

Strauss' proposal, however, brought out West Germany's ultra-right wing conservatives for a rare public display.

A petition demanding amnesty appeared this week in the weekly Deutsche National Zeitung, an ultra-right wing newspaper. It was signed by Winifred Wagner, the grand-daughter of Hitler's favorite composer, Richard Wagner, Ulrich Rudel, Hitler's favorite dive bomber pilot; Arno Breker, one of the rocket researcher favorite sculptors; rocket researcher Hermann Oberth and various other person including the former defense lawyers for Adolf Eichmann, the SS officer charged with carrying out the Jewish liquidation, and for Hitler's unlucky successor in the final days, Adm. Karl Doenitz.

The original statute of limitations on crimes of murder making it impossible to prosecute after 20 years, goes back to the last century, Because of post-war pressure from various groups of Nazi victims, it has been extended twice by the Bonn government because of its obvious link to war crimes rather than just civil murder cases.