The U.S.-backed military officers ruling Haiti appear to have lost much of the broad public support they held after taking over six weeks ago from the family dictatorship of Jean-Claude Duvalier.

In a country boiling with a largely leaderless yearning for swift and radical change, diplomatic sources said, the growing resentment against the military has increased risks of further instability and violence that could frustrate efforts to plant democracy here for the first time in a generation.

The Roman Catholic Church and the military were the principal institutions still in place after Duvalier's repressive rule crumbled. The church leadership, which was active during agitation against Duvalier, now has pulled back and civilian leaders have been slow to emerge.

Haitians and foreign diplomats said the shift in public mood against the Army has developed mostly from two roots:

First, Lt. Gen. Henri Namphy and his National Council have given the impression of moving slowly and even reluctantly to shed carry-overs from the Duvalier era and prosecute those guilty of abuses under the dictatorship.

Second, the Army last week cracked down on demonstrating mobs here, killing several youths and beating many more with rubber truncheons, after a traffic incident involving a bus driver and an off-duty officer mushroomed into an angry confrontation.

"The Army has no right to beat civilians," said Charles Leonel, 17, at a demonstration today outside the presidential palace. "It is the same regime in there as it was with Duvalier. The military has to get out of there."

Later today, bands of youths closed down businesses in the city center by burning tires, tipping over garbage bins and erecting rock barricades. Police downtown appeared to hold back, and no other violence was reported there.

"Namphy is well intentioned," Leonel said later today. "He's not ambitious. He may be the only man in Haiti who is not trying to become president. And he really believes in democracy. That's good, but he's only done half the job."

Gerard Gourgue of the Haitian Human Rights League, who resigned Thursday from Namphy's five-man council, said he walked out because the military leadership showed "too much slowness" in meeting popular demands for change. He cited demands for prosecution of Duvalier's associates in human rights abuses.

A knowledgeable source said Gourgue quit after several private warnings despite pressure from the U.S. Embassy to remain. The Reagan administration, which has strongly endorsed Namphy's rule, was eager to preserve the council's only member known for opposition to Duvalier during the dictatorship.

"I should have been able to make the demands of the people concrete," Gourgue said in an interview, adding that he could no longer give his "moral guarantee" to Namphy's rule. "The people are not only impatient. They are angry. And theirs is an anger I find legitimate."

At least two fliers circulating here have demanded that Gourgue be installed at the head of a civilian provisional government to replace Namphy's council. The authorship of these documents was uncertain. One was signed "the sovereign people."

Gourgue indicated that he is weighing the possibility of running for president, noting that he could not assume such a role from within the council because its members pledged not to seek political office.

Gourgue's resignation Thursday coincided with the shooting of at least four persons by security forces after the traffic incident, although he said the two developments were unconnected. In any case, violent protests broke out the next day. Apparently in response, Namphy reorganized the council to drop members most closely identified with Duvalier.

The new council consists of Namphy, Col. Williams Regala and Foreign Minister Jacques Francois. In effect, this left Namphy and the Army in charge, as they have been since Duvalier fled on Feb. 7.

Regala, who heads the key ministries of interior and defense, has long been a friend and follower of Namphy, a well-connected Haitian explained. Francois, a septuagenarian described by one observer as "geriatric," is expected to have little influence, diplomats here said.

Despite demands for swift signs of change from demonstrating youths and his own advisers, Namphy has not yet named the "consultative corps" that he announced Feb. 25 would elect a constitutent assembly to pave the way for elections. The U.S. Embassy also has urged that he set a date for the elections, even if it is remote, a knowledgeable source reported.

Namphy announced nomination of five new ministers today, extending the council's reorganization into the administrative ministries. He accompanied the announcement with a renewed pledge to turn over power to an elected government as soon as possible.