Jeremy Kinsman, of the Canadian Embassy here, was identified incorrectly yesterday. He is a minister at the embassy. In addition, comments by Kinsman referring to the evacuation of foreigners from the island of Grenada applied only to Canadian citizens there.

The Reagan administration yesterday refined the rationale for its Tuesday invasion of Grenada, stressing repeatedly that its uncertainty over who was running things on the island made the situation "a floating crap game" and left no other option.

Officials said they therefore ignored diplomatic notes from the Cuban government and from Gen. Hudson Austin, commander of the Grenadan army and a leader of last week's bloody coup, to the effect that American residents were in no danger and that anyone who wanted to leave could do so.

They also discounted a Grenadan promise to the Canadian government that it was safe to send a chartered plane for its citizens. An airline official said he was instructed Sunday night that all air and sea links to Grenada were suspended.

The administration also rejected charges that the invasion was illegal, saying that the United Nations Charter and the Rio Treaty of the Organization of American States allow "collective action pursuant to regional security treaties." U.S. withdrawal from Grenada will have to await the evacuation of all civilians who wish to leave and the return of "peace and security" to the island, according to State Department spokesman John Hughes.

Asked what that meant, he said, "It's something you know when you see it."

These arguments apparently won over an early critic, Charles R. Modica, chancellor and founder of the St. George's School of Medicine. Modica had said Tuesday that he thought President Reagan was "very wrong" in saying the invasion was necessary to protect Americans among the school's 650 medical students from the possibility of being held hostage or otherwise endangered after last week's coup. Yesterday, Modica said he had changed his mind.

A private State Department briefing gave him "new information I was not aware of," he said. "I found out that the people I had been dealing with in the Grenadan government were not fully in charge of that government and therefore could not guarantee the safety of Americans . . . . I feel Mr. Reagan was justified in making the decision he made."

White House spokesman Larry Speakes told reporters that the administration "had very real fears of a hostage-type situation involving student lives." A diplomatic note from Austin, received at the U.S. Embassy in Barbados at 2 a.m. Monday promised that all U.S. citizens would be safe, Speakes acknowledged. Hughes confirmed that notes from the Cuban government said the same thing.

"We didn't believe anything coming out of there. It was a floating crap game and we didn't know who was in charge, and I don't think they knew who was in charge," Speakes said. He noted that, although the Grenada message came from Austin, "his control of the Revolutionary Military Council was never established," and that Governor-General Sir Paul Scoon "was the remaining legitimate authority, and not the council."

Therefore, Speakes continued, "We replied Oct. 25 Tuesday that we could not respond to the message." He said that note went out around 1 a.m., six hours after Reagan had signed the order to invade the island.

Speakes said the invasion "could have stopped at any time if we had some assurances that our people would be safe." But the actions of the Grenadan government spoke louder than their words, he continued: "We didn't trust them, nor did their neighbors, so consequently any assurances they gave us in our opinion weren't worth two cents."

Reagan's letter to Congress justifying his action under the War Powers Act followed this theme, citing "a vacuum of authority" on the island.

Two political officers from the U.S. Embassy in Barbados were promised the run of Grenada to check on Americans there, but had difficulty getting in on Saturday.

Once there, they had trouble getting around, contacting people and getting out, Hughes said. They found 100 medical students who "said they would like to leave the island but were unable to," because no airplanes had been allowed to land even though Grenadans gave assurances that landings would be permitted, Hughes continued.

He said students' concerns, diplomats' difficulties with Grenadan officials and the closed airport were part of "the difference in the pronouncements of those who claimed to be in control of Grenada and the actions that in fact they took."

The Canadian government chartered a 48-seat twin-engine airplane from Leeward Islands Air Transport (LIAT), the only airline serving Grenada, to evacuate the estimated 30 Canadian citizens in Grenada Monday morning, according to LIAT general manager David Jardine. He said he was instructed Sunday night "by the Caribbean heads of government that they had taken a decision to suspend all air and sea links to Grenada."

Jeremy Kinsman, first secretary of the Canadian Embassy, said that his government also has had a Boeing 707 jet waiting for two days in Barbados to go to Grenada, but was told by U.S. military officials yesterday "that all foreign civilians, including Americans, were safe, and therefore evacuation per se was no longer a priority."

The State Department said in a formal statement that it had felt "increasing concern" over the Grenadan situation when the Organization of Eastern Caribbean States (OECS) met Friday in Barbados "and determined that the collapse of government on Grenada posed a threat to the security and stability of the region. The acting military council did not purport to be a government. The OECS members decided to take necessary measures in response to this threat and sought the assistance of friendly foreign states to participate in a collective security force."

Hughes, reading from the statement, said that such forces are consistent with both the OAS and the U.N. charter. The OAS charter "specifically allows OAS members to take collective action pursuant to regional security treaties" like the OECS treaty, Hughes said, while the U.N. charter's Article 52 provides for "regional arrangements . . . relating to the maintenance of international peace and security as are appropriate for regional action."

Hughes denied, as other officials had earlier, that the United States had in any way contacted the OECS nations first or suggested that the alliance invite U.S. participation.

Rep. Les Aspin (D-Wis.), chairman of a House armed services subcommittee, said he thought agreeing to the OECS request was "a terrible, terrible precedent."