Exactly one month after Herbert Kappler was discovered to be missing from his room at the Celio military hospital in Rome, the escape of the Nazi war criminal is threatening to cause a major political crisis here.

Six political parties, including three groups that support the minority Christian Democratic government, demanded this week that Minister of Defense, Vito Lattanzio, resign.

Because of unexpected Communist support for the resignation demand, there was concern here that the 13-month-old government of Giulio Andreotti, which depends on Communist support, may be in trouble.

The Kappler escape is so deeply felt here that for two days this week the halls of Italy's Chamber of Deputies echoed with demand for lattanzio's resignation and laments over Italy's humiliation and wounded national honor.

Despite their differences on other matters, exponents of parties as far apart ideologically as the Communists and the neo-fascists loudly agreed that Lattanzio, the commander-in-chief of Kappler's military guard, bears the final political responsibility for the Aug. 15 escape.

A 47-page speech by Premier Giulio Andreotti Tuesday that sought to exonerate his defense minister and explain why Kappler had been transfered last year from a prison to a lightly guarded hospital room did little to soothe the ruffled feelings of scores of Italian deputies and senators.

"The escape was a national embarassment," said a member of the Socialist Party, one of those demanding that lattanzio step down. "But it's even more embarrassing that 30 days later the government still doesn't know just how Kappler got away."

Ever since Kappler, 70, who is suffering from cancer, escaped with the help of his wife, Anneliese, a variety of theories have circulated as to just how the ailing former commander was able to flee.

The first version, that Anneliese wheeled him out of the hospital in an oversize suitcase on wheels, has now been discounted. Later there was speculation that the West German secret services were to blame and that Kappler had been faking and did not have cancer after all.

In an article sold to the Italian weekly, Oggi, Mrs. Kappler said she used alpine rescue gear to lower her husband from his hospital room's window. Other reports say Kappler may have simply walked out while his wife distracted the guards with wine and cake.

Daring escapes of the past, like those of Renaissance sculptor Benvenuto Cellini from Rome's Castel Sant' Angelo and of Cassanova from a Venetiian jail, won widespread approval here. But a grudging admiration for the Kappler feat appears to have been blurred by a sense of humiliation over an escape engineered by a 52-year-old woman and the ambarrassment suffered by the usually prestigious corps of "carabinieri", or national police, three of whom have been charged with negligence.

Strong feelings about Nazism and Fascism still exist here. The Communists reportedly changed their position on the resignation of Lattanzio after encountering considerable grassroots dissatisfaction with the cautious policy adopted by the party immediately after the escape.

Reports from Caserta, near Naples, say that when the party's new stand on the Kappler issue was announced there on Sunday, the crowd broke into frenetic applause.

The Communists' decision to add their voice to the general cry for political blood also reflects the party's growing irritationwith their principal partner, the Christian Democrats.