KUALA LUMPUR, MALAYSIA—Investigators are looking for four North Korean men who flew out of Malaysia the same day Kim Jong Nam, the North Korean ruler’s outcast half-brother, apparently was poisoned at an airport in Kuala Lumpur, Malaysian police said Sunday.

Since Kim’s death last week, authorities have been trying to piece together details of what appeared to be an assassination. Malaysian police have so far arrested four people carrying IDs from North Korea, Malaysia, Indonesia and Vietnam.

Malaysia’s deputy national police chief, Noor Rashid Ibrahim, said four other North Korean suspects were on the run. He said that the men had arrived in Malaysia on different days beginning Jan. 31, and that they had all flown out of the country last Monday, when Kim died.

“I am not going disclose where they are,” he told a room packed with journalists, adding that Interpol was helping with the investigation.

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Noor Rashid showed photographs of the four men, who were travelling on regular — not diplomatic — passports and are ages 33, 34, 55 and 57.

He also said there were three other people police wanted to question. He said that one was North Korean, but that police had not yet identified the other two. It wasn’t clear if they were suspects or simply wanted for questioning.

A rotund man in his mid-40s, Kim Jong Nam was waiting for his flight home to Macau when, authorities say, he was set upon by two women. He sought help at an airport customer service desk and said “two unidentified women had swabbed or had wiped his face with a liquid and that he felt dizzy,” Noor Rashid said.

Kim died en route to a hospital after suffering a seizure, officials say.

Noor Rashid said Sunday that he expected autopsy results to be released within days. “We have to send a sample to the chemistry department, we have to send a sample for toxicology tests,” he said.

Investigators also want to speak to Kim Jong Nam’s next of kin to formally identify the body. He is believed to have two sons and a daughter with two women living in Beijing and Macau.

“We haven’t met the next of kin,” Noor Rashid said. “We are trying very hard to get the next of kin to come and to assist us in the investigation.”

Noor Rashid said charges against the four suspects in custody would be determined by prosecutors.

According to police, the Vietnamese woman works at an entertainment outlet; the Indonesian woman is a spa masseuse; the Malaysian man, who is believed to be a boyfriend of the Indonesian woman, is a caterer; and the North Korean man works in the information technology department of a Malaysian company.

The Indonesian woman has told investigators that she was duped into thinking she was part of a comedy show prank.

Police said the North Korean man’s work permit had expired Feb. 6, a week before Kim’s death.

The case has raised tensions between Malaysia and North Korea. Pyongyang demanded custody of Kim’s body and strongly objected to an autopsy. The Malaysians went ahead with the procedure anyway, saying they were simply following procedure.

Kang Chol, North Korea’s ambassador to Malaysia, said that Malaysia may be “trying to conceal something” and that the autopsy was carried out “unilaterally and excluding our attendance.”

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“We are investigating a case of murder ... we just follow our rules and regulations,” Noor Rashid said.

South Korea has been quick to blame its enemies in North Korea for Kim’s death.

“Considering North Korea has so far committed crimes against humanity and terror acts, we, together with the international community, are closely watching this brutal, reckless incident with serious concerns,” South Korean Unification Ministry spokesman Jeong Joon Hee told reporters in Seoul on Sunday.

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