The five-day crisis over the fate of Americans in Uganda eased markedly yesterday after Ugandan President Idi Amin told the Americans they were free to leave the country.

There were indications that the move, welcomed in Washington by Secretary of State Cyrus Vance, followed pressure exerted on Amin by several Arab and African governments at the request of the United States.

Amin's announcement early yesterday countermanded his surprise order Friday that Americans living in Uganda could not leave the country until they met with him. The meeting has been postponed twice, however, and observers in neighboring Kenya speculated that it would never come off.

Uganda Radio said that President Carter had appealed to "a number of Arab and African states" to urge Amin to insure the safety of Americans, Washington Post special correspondent Roger Mann reported from Nairobi, Kenya.

Special envoys from Saudi Arabia, Zaire, Rwanda and Sudan arrived in Uganda during the past two days with messages from their governments concerning the American residents' situation, the Manchester Guardian reported from Nairobi.

Uganda Radio said Amin had commended the Rwandan delegation for coming to him for information and quoted him as saying, "Some African leaders have become telephone operators and messengers of America because they do not want to get correct information on what has happened in Uganda."

In Washington, the State Department confirmed reports that it had made contingency plans to evacuate the Americans on a Swiss charter aircraft if they had been ordered to leave.

The evacuation plan has now been dropped, State Department spokesman Frederick Z. Brown said, adding, "Our concern has eased." He declined, however, to say whether the United States regards the matter as closed.

Vance said yesterday morning that he expects some of the 240 American missionaries, teachers and businessmen living in Uganda to leave now that Amin has lifted restrictions on their movements.

The senior, Ugandan diplomat in Washington, acting Charge d'Affaires Paul Cherubet, said that Amin had called off his meeting with Americans, scheduled for Wednesday, to defuse tensions building up between the two countries.

Cherubet told reporters that "overreaction" by U.S. officials and news media were among the factors behind the cancellation. He also cited the presence in the Indian Ocean of a U.S. naval task force on maneuvers.

"The tensions were building between a big power and a small country . . . We decided to forget everything and rearrange it later," he said.

A New Jersey tourist, apparently the first American to leave Uganda since the five-day crisis began, arrived in Nairobi yesterday. "I was a happy man when I stepped across the border into Kenya," said Robert Shinn, 25, of Spring Lake Heights, N.J.

Shinn, interviewed in Nairobi wearing a "Tourism in Uganda" T-shirt, said he took a bus to the Kenyan border after West German diplomats who handle American affairs in Uganda told him the travel ban applied not to tourists but to Americans living in the country.

Meanwhile, Uganda Radio reported that the Special envoys from Saudi Arabia, Zaire, Sudan and Ruwanda are now touring Uganda's game parks.

The official radio provides a taste of the Alice-in-Wonderland quality of Amin's Uganda. Yesterday morning's news that the Americans were free to leave was preceded by a loud rendering of "The Teddy Bears' Picnic" in English, the Ugandan national anthem and a reference to Amin as "His Excellency, Life President Idi Amin Dada, VC, DSO, MC and commander-in-chief of the Ugandan armed forces."