Two of the politicians competing for power in Haiti after the assassination of President Jovenel Moïse are close to an agreement that they hope will stabilize the embattled Caribbean nation and lead to fresh elections, one of the politicians involved said.

Ariel Henry, a neurosurgeon who was appointed Haiti’s prime minister a little more than a day before Mr. Moïse’s death, said Monday that he and Claude Joseph, the interim prime minister who asserts he leads the country, are in talks to cut a deal “in the coming hours.”

“There will be an agreement,” Mr. Henry, a former interior minister, told The Wall Street Journal in a phone interview. “We are putting the Haitians first, it is a solution that I think will please the Haitian people.”

He wouldn’t provide details of the possible agreement, but the claims to power by Mr. Henry and Mr. Joseph have complicated the political uncertainty on the island. “There will be an agreement that will enable the country to leave this area of instability,” Mr. Henry said.

Mr. Joseph couldn’t be reached for comment. But a close aide to Mr. Joseph said Saturday that both men were in constant communication to reach an agreement. “The last thing we want right now is a power struggle,” he said.

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At a media event, Haitian authorities presented guns, machetes and a group of people they said were linked to the assassination of President Jovenel Moïse. Suspects include two U.S. citizens, according to officials in Port-au-Prince. Photo: Jean Marc Herve Abelard/Shutterstock The Wall Street Journal Interactive Edition

His comments came as the National Security Council in Washington recounted to reporters a trip over the weekend to Haiti by officials from Homeland Security Department, the State Department and the National Security Council. The Americans met with both Mr. Henry, whom Mr. Moïse had named prime minister, Mr. Joseph and Senate President Joseph Lambert, a third official vying for power.

The U.S. shied away from signaling support for one leader over the other. Last week, State Department spokesman Ned Price said the U.S. had been working with Mr. Joseph, referring to him as “the incumbent in the position.”

Separately, a U.S. Drug Enforcement Administration official said Monday that a suspect in the assassination had been a confidential informant for the agency. The official declined to identify the suspect but said a DEA agent helped facilitate his surrender to local authorities.

Shortly after Mr. Moïse’s July 7 killing, the official said, the suspect reached out to his contacts at the DEA. One of them, assigned to the agency’s office in Haiti, then urged the man to surrender to local authorities, the official said.

The DEA agent and a representative from the State Department then shared information with the Haitian government that led to the arrest of the suspect, who is no longer an informant for the agency, the official said.

The U.S. Justice Department said late Monday that it was assisting Haiti’s national police force with its investigation into the assassination.

“The department will also investigate whether there were any violations of U.S. criminal law,” spokesman Anthony Coley said.

Haiti is on the brink of anarchy less than a week after the brazen attack. A government with a single voice would mean more legitimacy to organize scheduled elections later this year, which the U.S. is advocating.

The U.S. and other countries have urged Mr. Henry and Mr. Joseph to collaborate and avoid an adversarial relationship that would worsen an already fragile situation.

Mr. Moïse appointed Mr. Henry last Monday in one of his last moves as president. Mr. Joseph publicly congratulated Mr. Henry. Then came the killing in Mr. Moïse’s residence.

At the moment, there is no apparent way out of a political crisis in which at least three men are claiming leadership. There are only 10 lawmakers in parliament, after terms for lower house members and most senators expired and no new elections were held. The president of the Supreme Court, who could have settled the dispute, died from Covid-19 last month.

Eight lawmakers declared on Friday their loyalty and recognized Mr. Lambert, the head of Haiti’s dismantled senate, as provisional president and Mr. Henry as prime minister.

Mr. Joseph, who effectively controls the police and the bureaucracy, has maintained that he should be in charge until elections for president, parliament and regional leaders are staged, possibly this fall.

Mr. Henry said elections will be held “as soon as possible.” Although he has pushed to be recognized as prime minister—and thus the leader of the country because of the death of the president—Mr. Henry said he won’t run for president in future elections.

—Sadie Gurman contributed to this article.

Write to Juan Montes at juan.montes@wsj.com