UNITED NATIONS (Reuters) - Congolese President Joseph Kabila told the annual gathering of world leaders at the United Nations on Saturday that he would ensure those responsible for killing two U.N. investigators earlier this year would be punished.

Michael Sharp, an American who was coordinator of an independent sanctions monitoring group, and Zaida Catalan, a Swede, were killed in central Congo on March 12 while carrying out investigations for a report to the U.N. Security Council.

The bodies of Sharp and Catalan were found in a shallow grave two weeks later.

"We are determined to ensure that light is shed on the exact circumstances of this crime and to ensure that this horrendous act ... will not remain unpunished," Kabila said.

"This is exactly what open public court processes have been working toward for several weeks now following the arrest of the majority of the suspects of these crimes," he told the 193-member General Assembly.

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Congolese authorities have arrested nine suspects in the killings but some Western governments and rights groups are skeptical that the real masterminds have been identified.

An internal U.N. inquiry found that Sharp and Catalan were murdered by a group of Congolese, likely militia members from central Democratic Republic of Congo, but an absence of evidence "does not preclude the possibility that others are involved."

At a U.N. Security Council meeting last month, the United States, Britain, France, Sweden and Japan urged U.N. Secretary-General Antonio Guterres to establish a follow-up investigation to determine responsibility.

Guterres has said he planned to discuss the establishment of a "follow-on mechanism" to the board of inquiry with Congo officials and council members.

"The most effective would be the integration of independent experts into the Congolese system. I do not know whether it will be possible or not," Guterres told reporters last week.

"Otherwise, we will take our own initiative: our colleagues in the Department of Political Affairs are making all the necessary consultations to put in place the system that can be as effective as possible for the truth to be known," he said.

ELECTIONS

In the central Congo Kasai provinces, where Sharp and Catalan were killed, an insurrection by the Kamuina Nsapu militia, which demands the withdrawal of Congolese forces from the area, has driven 1.4 million people from their homes and killed more than 3,000 since August last year.

Kabila said the country had "fallen victim to terrorist attacks" and that a "mystical religious tribal militia is using the civilian population, including children as a human shield."

Kasai poses Congo's biggest security challenge and is the scene of a growing humanitarian disaster in a country where militia violence since Kabila refused to step down in December has raised fears of a slip back into civil war.

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Kabila also told the U.N. General Assembly that Congo had so far registered 42 million of 45 million voters and that the National Election Commision would "soon publish the electoral calendar and timelines."

"Despite this progress, challenges in organizing elections in my country remain great, both on the logistical level, as well as on the financial, security and legislative one," he said. "I can affirm that we are most certainly moving towards credible, transparent and peaceful elections."

He did not say if the vote would take place this year, as required by a deal with Congo's opposition that allowed him to stay in power beyond the expiry of his mandate last December.

(Reporting by Michelle Nichols; Editing by Lisa Von Ahn and James Dalgleish)