Personal pleas from Prime Minister Ian Smith, a reported long distance telephone call from an American industrialist and pressure from a strong faction in his own party are weighing on Bishop Abel Muzorewa not to follow through on his threat to abandon Rhodesia's six-week-old multiracial government.

These developments, plus a hurried and hushed executive council meeting of the four interim government leaders yesterday - requested by Muzorewa - are evidence of behind-the-scenes efforts to avoid a pullout by Muzorewa and his United African National Council Party.

Despite the concern shown by the pleas, the general reaction to Muzorewa's threat, however, has been: "Muzorewa has done things like this before and he always comes around."

Muzorewa's party said Sunday it would decide next Sunday whether to withdraw from the multiracial government set up March 3 by Murzorewa, Smith, the Rev. Ndabaningi Sithole and Chief Jeremiah Chirau. It was reacting to the firing of Byron Howe, a black justice minister appointed to his post by Muzorewa's party.

Hove was dismissed last week by the executive council of the new government for urging fundamental changes in the police and judiciary systems. Muzorewa said he did not approve of the decision. His party demanded Hove's reinstatement and said if he was not reinstated, three white officials who criticized Hove's statements should resign.

According to sources in Muzorewa's party, Smith contacted Muzorewa in person on Saturday and telephoned him again on Sunday to urge that he continue his participation in the government.

A similar request to Muzorewa was reportedly made by telephone by E.F. (Andy) Andrews, a vice president of Allegheny Ludlum Industries Inc. of Pittsburgh, according to a black nationalist source.

(A spokesman for Andrews, reached in Pittsburgh yesterday said that Andrews had not talked to Muzorewa for "a week or more." Andrews, according to the spokesman, "said he did not see how he could have had any influence" on Muzorewa in recent days "because he has not been in touch with the bishop or any of his executive council since reading about the dismissal of Hove in the newspapers.")

Allegheny Ludlum was one of the principal buyers of Rhodesia's high-quality chrome, a product American companies are no longer legally allowed to purchase since congressional repeal of the Byrd Amendment last year.

Andrews reportedly helped bring about the so-called internal settlement setting up the present government by influencing Muzorewa to accept provisions some members of his party were objecting to.

Muzorewa is also under pressure from a strong faction in his party that does not favor pulling out of the government, which it helped set up. According to knowledgeable observers, this faction is more influential in the party than a more militant wing that is urging Muzorewa to drop out and possibly make an alliance with the guerrilla leader, Robert Mugabe.

The internal settlement was reached by Smith and black leaders living in Rhodesia in an effort to forestall efforts by the United States and Britain to bring about black majority rule in which nationalist guerrillas now based outside Rhodesia would have a key role.

Another infication of the seriousness with which Muzorewa's threat is being taken by some is that fact that an emergency Executive Council meeting was held yesterday, as Muzorewa's party requested. No announcement was made of the meeting nor of what was discussed. One white government official said, "they want to play this down. They don't want to speculation."

A withdrawal of Muzorewa could severely cripple the young experiment in multiracial rule here. Muzorewa is thought to hold the most support among Rhodesia's 6.7 million blacks.