The Panamanian Fifth Company is stationed at Fort Amador, along with American troops, and Major Giroldi feared the Panamanian troops there would defend General Noriega. The Seventh Company is to the southwest of Howard Air Base, and Major Giroldi was also concerned about that unit. Worrisome Statements

Administration officials said Major Giroldi did not want more American involvement. He said the coup would take place on Monday, but would begin only if General Noriega was not at his headquarters. He indicated that the rebels simply wanted the general to retire honorably.

Major Giroldi's statements worried the Americans and made them suspect that they would not be able to get General Noriega out of the country to face drug and racketeering charges filed by two Federal grand juries in Florida in 1988. ''That had an impact later on,'' Mr. Cheney said.

Mr. Cheney and others said that to avoid the possibility of a trap Major Giroldi was not given any commitments of American help. Monday, Oct. 2 Morning, Washington

At 2:30 A.M., Mr. Cheney was awakened by Gen. Colin L. Powell, newly appointed as chairman of the Joint Chiefs of Staff but not yet sworn in to his post, and was told about the contact Sunday night in Panama City. Mr. Cheney telephoned Brent Scowcroft, Mr. Bush's national security adviser, and around this time Mr. Cheney approved sanctuary for Major Giroldi's family. ''All of us agreed at that point that we simply had very little to go on,'' Mr. Cheney later said.

Throughout the day, Administration officials appear to have acted in a cloud of confused and vague information about the events in Panama and an atmosphere of mistrust that may have predisposed them not to throw much support behind Major Giroldi.

Coup reports from Panama were not uncommon, and Major Giroldi was not on the Pentagon's list of Panamanian officers who were considered capable of seizing control and holding it; he was a confidant of General Noriega and had been responsible for putting down the last coup attempt, in March 1988, just after the Federal indictments against General Noriega. Mr. Cheney and others feared they were being ''set up.''