Secretary of State Cyrus R. Vance sought yesterday to smooth the feathers of his predecessor, Henry A. Kissinger, after they were badly ruffled by reports of anonymous Carter administration criticisms of Kissinger's role in the Iran crisis.

Last week Vance invited Kissinger to come to the State Department for a full briefing on the situation in Iran. During the 75-minute meeting yesterday, administration sources said, Vance sought to calm Kissinger, who was described as enraged by an article in Saturday's Boston Globe.

The Globe quoted "a high State Department official" as saying that Kissinger threatened to "hold the Carter administration accountable for the death of the deposed shah if the exiled Iranian ruler was not permitted to come to the United States for cancer treatment."

This account was publicly and privately denied yesterday, by Kissinger and by senior administration officials. They noted that Kissinger was traveling at the time the White House decided to allow the shah into the United States for medical treatment, and they said he had not contact with the State Department or the White House on the matter.

(Earlier, Kissinger did press the administration repeatedly to allow the deposed shah to enter the United States.)

The Globe also quoted a senior aide to President Carter as calling Kissinger "a devious and dishonorable man" who attacks the president publicly in Iran, then calls the president's friends privately to say he supports Carter's handling of the crisis.

There were no denials of this quotation yesterday, and White House sources confirmed that this sentiment is held by senior officals there. However, other senior aides to the president sought to calm the situation, insisting that the White House wants no fight with Kissinger.

The flap illustrate the sensitive political problem Kissinger poses for the Carter administration. As one administration official noted last night, some White House officials believe Kissinger's support for SALT II is crucial to its prospects for Senate approval, so there is a great eagerness not to alienate him.

At the same time, administration officials cannot disguise their resentment of Kissinger's escalating criticism of Carter's foreign and defense policies. Last week in Austin, Tex., Kissinger told a Republican Governors' Conference meeting that the fall of the shah was a disaster for America, and suggested that during the Carter administration other countries had learned that "there is no penalty for opposing the United States and no reward for friendship to the United States."

Last Friday's Wall Street Journal carried a report that Kissinger had treatened to withhold his final support for SALT II until the White House allowed the shah into the United States. White House press secretary Jody Powell denied this report yesterday, as other senior officals did privately.