Herbert Blaize, 66, a self-taught solicitor, was sworn in as Grenada's new prime minister today and vowed to give the island's 110,000 inhabitants "that kind of security they have a right to expect."

Blaize and his New National Party swept to a landslide victory in yesterday's elections, winning 14 of 15 seats in the House of Representatives.

The triumph, for an alliance understood by most Grenadians to enjoy U.S. backing, marked a visible endorsement of the Reagan administration's invasion here Oct. 25, 1983, that crushed what remained of a failed Marxist-oriented revolution.

Blaize, who concentrated his campaign on promises of stability, said at a victory news conference that the voting results represent rejection of "postures of the extreme left or postures of the extreme right."

The two-time head of the colonial government, prior to independence from Britain in 1974, promised to follow a moderate course designed to restore faith in the island's government institutions after the abuses and eventual self-destruction of prime minister Maurice Bishop's leftist rule.

Blaize's main challenger, the Grenada United Labor Party of former prime minister Eric Gairy, won the remaining seat. But the victor in that district, Marcel Peters, said after conferring with Gairy that he will resign.

Peters said the party is charging irregularities in the vote. Diplomatic sources said the constitution calls for a by-election within several weeks if Peters follows through on his threat, raising the prospect that Blaize could control all 15 seats.

Bishop's remaining followers, in the Maurice Bishop Patriotic Movement, who failed to gain a seat, have accused Blaize for some time of receiving help from the CIA. They apparently refer to funds provided by two American private groups with ties to Republican politics and a third linked to the AFL-CIO.

Blaize dismissed the charges of irregularities as carping of "disgruntled wretches" who refused to accept defeat. He noted that observers from the Organization of American States and the British High Commission for the eastern Caribbean, on hand to guarantee fair balloting, reported no serious violations of procedure.

"They have seen for themselves that the conduct of the election over the last day was above reproach," Blaize declared.

Blaize said he would begin consultations immediately to form a Cabinet. He also must name 10 persons to the 13-member Senate that has powers similar to those of the British House of Lords.

Under Grenadian rules, the opposition party normally names the other three members, but Peters' resignation threat left disposition of those seats unclear.

Robert Graham, an attorney who withdrew from Blaize's alliance in a dispute two months ago, predicted the most serious opposition will come from within the coalition, formed of Blaize's own party and two others whose leaders have ambitions of their own.

Gairy remained for most of the day in his pink bungalow above the harbor as glum supporters filed in and out. As he conferred with visitors, a man in a white cassock, carrying a light wooden walking stick and a small Grenadian flag, marched back and forth in the garden chanting unintelligibly.

Blaize announced that he has sent a message to President Reagan asking him to maintain the 250 U.S. troops here "until such time as we could have a fully equipped and trained security force."

[The White House quoted Reagan as declaring, "We applaud the Grenadian people for their peaceful, orderly and genuinely democratic exercise of popular sovereignty. . . . We look to working closely with the new government of Grenada."]

Similar messages went to leaders of Caribbean islands who have contributed personnel to a 450-man Caribbean force maintaining order on the island as Grenadians are trained, Blaize said.