Ten days after taking power in the English-speaking Caribbean's first coup d'etat, the new government of Grenada appears firmly in control and has been recognized by neighboring island nations, the United States and Britain.

Caribbean members of the British Commonwealth, to which Grenada also belongs, continue to express private concern that the coup set a bad precedent in a region with a long domocratic tradition.

But acceptance of the new administration, one Caribbean diplomat said, has been greatly helped by two things. Since the March 13 coup, the diplomat said, Marurice Bishop, head of the new government, has "made all the right moves" to reassure Grenada's neighbors that democracy will be restored through early elections.

At the same time, he said, few in the Caribbean were sorry to see Bishop's predecessor, Prime Minister Sir Eric Gairy, thrown out.

Despite a "certain amount of rhetoric" accusing Bishop's New Jewel Movement of leftist tendencies ranging from moderate socialism to Marxism, the diplomat said, "one must start off in the Caribbean by saying that anybody who had something against Gairy can't be all bad."

A former cane-cutter, school teacher and labor organizer, Gairy, 57, controlled politics on the 133-square-mile island since the early 1960s and continued as prime minister after independence from Britain in 1974.

An outspoken believer in extrater-restrial beings who had become somewhat of an international character by virtue of regular United Nations speeches on the subject, Gairy had domestic policies that included repression of opposition groups, particularly at election time. Many political leaders in the region considered Gairy an embarrassing reflection on the Caribbean.

According to Kendrix Radix, the 37-year-old attorney and member of Parliament who arrived in Washington as the new government's ambassador last week, new voter registration lists are already being compiled in Grenada, and elections will be held within the year, if not sooner.

"I want to make it clear that this is a provisional government," Radix said. He said that the government would be seeking "international assistance" for agriculture and tourism projects, that it had no plans to interfere with the ownership of private property on the island, and that 'we want good relations with everybody."

Gairy, who has been in the United States since the day before the coup, has accused the New Jewel Movement of being communist and pointed out that Bishop visited Cuba.

"Bishop has visited the United States, England, Scandanavia and all of the West Indies," Radix said. "I don't see why anyone should attach great importance to Maurice Bishop's visits to Cuba."

Arms used during the brief insurrection, in which one government soldier and one policeman were killed, Radix said, were not received from any other government. "Our party is about the reestablishment of democratic rights by our people," he said.

Other Caribbean governments, as well as the United States, have indicated they will be closely watching to see if the new government keeps its promises.

In statements released following a post-coup foreign ministers' meeting, Jamaica, Barbados, Guyana and associated English-speaking Caribbean states announced "de facto recognition" of the Bishop government.

The governments, however, called for an "early early return to constitutional practices through free and fair elections," respect for political opponents and the continuation of "fundamental rights and freedoms" in Grenada.