President Carter joined a world-wide chorus of government leaders and private organizations yesterday calling on the government of Pakistan to spare condemned former Prime Minister Zulfikar Ali Bhutto from execution.

State Department spokesman Hodding Carter said the U.S. ambassador in Islamabad, Arthur W. Hummel Jr., had delivered a message from President Carter to Pakistani President Mohammed Zia ul-Haq about Bhutto's situation.

Although he declined to reveal the contents of the message, the spokesman added: "The United States government hopes Mr. Bhutto's life will be spared."

Pakistan's supreme court, by a 4-to-3 vote, yesterday upheld the death sentence imposed on Bhutto after his conviction for ordering the murder of a political rival four years ago. Bhutto, now 51, was deposed by Zia in a 1977 military coup.

U.S. sources, while confirming that Carter's message was an appeal for clemency, said it was not being made public because of its personal nature and because it is U.S. policy not to disclose personal communications between heads of state.

Leaders of other countries were less guarded in making known the nature of their appeals on Bhutto's behalf. British Prime Minister James Callaghan, for example, told the House of Commons:

"I have today officially made representations to Gen. Zia to ask him that he should as an act of clemency spare the life of Mr. Bhutto. The consequences of clemency would be more beneficial to his country than the strict application of the law."

Callaghan, who met Zia on a visit to Pakistan last year, said he since has exchanged several letters with the Pakistani president about Bhutto's fate.

Similar messages were sent to Zia from Scandanavia by Swedish Premier Ola Ullsten and Norwegian Prime Minister Odvar Nordli. Ullsten said in a cable:

"My country opposes the death penalty and has for many years worked for its banishment... A decision by your excellency to commute the death sentence to less grave penalties would be welcomed the world over as a humanitarian act."

Premier Bulent Ecevit of Turkey, which traditionally has had close ties with Pakistan, also called for a pardon and said Bhutto could live in Turkey "if that will contribute to the setting up of a democratic regime in Pakistan."

In Australia, Foreign Minister Andrew Peacock said his government will "make representations" about commuting the sentence. He added, "Australia's expression of concern should not be interpreted as interference in the affairs of another government, but for humanitarian reasons, we feel compelled to ask for clemency."

Amnesty International, the London-headquartered international organization that works to free political prisoners all over the world, called for setting aside the death sentence and granting Bhutto a new trial.

In a cable casting doubt on the impartiality of Bhutto's trial, Amnesty International said: "The international press and observers attending the appeal hearing have expressed doubt about the impartiality of the bench trying the defendants.

"Unfortunately," the message added, "the supreme court hearing could not reexamine witnesses. Thus it could not investigate the defense claim that statements of prosecution witnesses were contradictory, that some have not been brought on record and that evidence was taken in a manner favorable to the prosecution. Such doubts can only be removed by a retrial of the accused."