KUALA LUMPUR, Malaysia—Suspected militants linked to Islamic State were stopped just short of attacking Saudi royals during King Salman’s recent trip here, Malaysian police said, dealing with a second high-profile plot after a hit squad allegedly led by North Koreans recently staged a brazen killing at the main airport.

“We got them in the nick of time,” Inspector General of Police Khalid Abu Bakar said. Three teams of militants had planned attacks on the Saudis, he said, but he declined to give details of their alleged plans. One group comprised four Yemenis, another an Indonesian and a Malaysian, and a third a lone man from an unspecified East Asian nation.

Malaysia, without specifying the targets, said the plotters were arrested between Feb. 21 and 26. Police said two of the men were directed by Muhammad Wanndy Mohamed Jedi, a Malaysian who joined Islamic State in Syria in 2015, in preparing a car bomb. The Indonesian arrested had previously been deported to Turkey after trying to enter Syria, police said.

Police said the East Asian suspect, believed to have been living in Malaysia on a student visa since 2011, had suspected links to a regional terrorist group that uses Malaysia as a transit point and safe haven.

The Saudi king has been leading an entourage of up to 1,500 people on a monthlong tour of Asia to strengthen ties with a region the kingdom sees as an increasingly valuable economic partner and as a hedge against an unpredictable U.S. government.

Malaysia was the first stop. The monarch traveled on to Indonesia and now is on a weeklong holiday on the resort island of Bali before heading to Japan, China and elsewhere.

A spokesman for Saudi Arabia’s Ministry of Foreign Affairs didn’t respond to a request for comment on Tuesday.

The foiled plot against the delegation underscores Islamic State’s ongoing campaign against the Saudi kingdom. The group has called for the downfall of the Saudi monarchy and, since the militant group’s rise in 2014, its loyalists have carried out a score of small-scale attacks in the kingdom.

Islamic State sees Saudi royals as heretics and enemies in part because of their longstanding alliance with the U.S. and the West. The Sunni Muslim terror group has also sought to challenge the Saudi monarch’s role as guardian of Islam’s holiest sites in Mecca and Medina.

In July, a suicide bomber killed four security guards near the Prophet’s Mosque in Medina, an attack that bore the hallmarks of Islamic State. It was one of three bombings that struck the kingdom within hours of each other on the eve of the Islamic holiday of Eid al-Fitr.

Saudi Arabia has confronted the threat of Islamic extremism before. Al Qaeda turned its wrath against the kingdom in the prior decade, a campaign that was effectively suppressed by Prince Mohammad bin Nayef, the current crown prince.

Prince Mohammed in 2009 narrowly escaped an assassination attempt by an al Qaeda suicide bomber who was posing as a reformed jihadist. The prince was slightly injured.

The alleged plot revealed Tuesday added to a long list of terror plots with connections to Malaysia, a fast-developing Southeast Asian hub for business and transit that has tried to shake a reputation as a haven for terrorists and illicit activity.

In January 2000, Kuala Lumpur was site of an infamous planning meeting for the Sept. 11 attacks of 2001, with the Federal Bureau of Investigation later calling Malaysia “a primary operational launchpad.”

Counterterrorism forces have feared that Islamic State will take root in the region, particularly among the Muslim populations in Indonesia, Malaysia and the southern Philippines. In January 2016, four Indonesian militants with links to Islamic State killed four people in downtown Jakarta. It was the group’s first attack in Indonesia, the country with the world’s largest Muslim population.

Malaysia recently was the scene of terrorism of a different sort. On Feb. 13, a hit team killed Kim Jong Nam, the estranged half brother of North Korean dictator Kim Jong Un, by smearing his face with a lethal VX nerve agent while he was waited in a crowded airport departures hall. Police believe four North Korean suspects in the murder plot escaped to Pyongyang, while three others are said to be in hiding at the North Korean Embassy.

Malaysia has since revoked visa-free travel for North Koreans and the two countries have expelled each other’s ambassadors. Pyongyank is now preventing its Malaysian visitors from leaving North Korea, and Malaysia has imposed the same restrictions on its North Korean tourists.

—Margherita Stancati in Dubai contributed to this article.