The extraordinary escape of a cancer-ridden Nazi war criminal from a Rome prison hospital to West Germany yesterday has now led to postponement of summit talks between West German Chancellor Helmut Schmidt and Italian Prime Minister Giuilio Andreotti.

In addition, the serious legal and emotional tangle the episode has created for both governments could produce a potentially ugly strain on relations that have otherwise been quite good.

Facing a mixture of public humiliation and anger over the escape of 70-year-old former Rome Gestapo chief Herbert kappler, Andreotti's office said today that it wanted "to prevent the visit of Chancellor Schmidt at a time when public opinion was deeply disturbed by the escape and could give rise to demonstrations that might unjustifiably be interpreted as a split in the solid friendship between the Italian and German peoples."

The Schmidt-Andreotti talks on economic and political affairs were to be held in Verona on Friday. They have now been put off until an unspecified time this autumn by mutual agreement, but at the request of the Italians, government spokesmen here and in Rome said today.

It was publicly announced late today that police have called off the search for Kappler and his wife, and senior officials said privately that the couple's whereabouts is known.

Officials indicated privately that Kappler would not be arrested because he is in such bad health that he couldn't move anyway, and that the constitution assures that he would not be extradited.

The decision not to arrest him was a state rather than a federal matter, officials said, and the courts not hte government, will decide whether there will be any legal proceedings against Kappler - judged to be highly unlikely.

Senior officials said Kappler would undoubtedly get his wish to stay in the Federal Republic and die here.

Last year, Kappler was granted provisional freedom by a military tribunal in Rome, but the decision caused such massive demonstrations by private citizens. Jewish groups, World War II partisan organizations and leftist groups that the decision was overturned.

Kappler had been serving a life sentence since 1948, when he was convicted of directing the murder of 335 Italian civilians in 1944 in reprisal fo the killing of 32 German soldiers in Rome by Italian partisans the day before.

The former officer, now emaciated and weighing barely 100 pounds as a result of his stomach cancer, frequently asked to be allowed to come back to his homeland to die. But he probably had little to do with his actual escape.

His wife, Anneliese, 52, described as "a rather robust woman," apparently fitted him into a large suitcase and spirited him out of his third-floor bed into a waiting car and along the roads through Austria or Switzerland to West Germany.

In Rome, officials said the goverment would soon formally ask the West Germans to extradite Kappler, which Bonn is virtually certain to refuse to do. Demonstrations in Italy. which in turn could produce the ill feelings that both countries would like to avoid.

West Germany's constitution specifically protects German nationals from being extradited, and Justice Ministry officials in Lower Saxony, where Mrs. Kappler lives, indicated today that there is no chance of Kappler's being sent back to Italy.

Theoretically, it was said, he could be put on trial again here - but that is also unlikely, because he has already served 29 years in jail and would undoubtedly also be judged physically unfit to stand trial.