Smoke from forest fires in Indonesia has choked neighboring Singapore and Malaysia, prompting Singaporean officials to press Jakarta for urgent action against the haze that has pushed the city-state’s air pollution to the worst level in 16 years.

The haze, blown toward the east and northeast from fires in Sumatra Island, first hit Singapore and peninsula Malaysia over the weekend and has lifted air-pollution indices in both countries into “unhealthy” territory. Iconic skyscrapers in Singapore’s business district remain shrouded in smog Tuesday, with some residents starting to take precautions by donning masks and staying indoors.

In Singapore, the three-hour Pollutant Standards Index—a measure developed by the U.S. Environmental Protection Agency—peaked at 155 Monday night, the highest reading notched since September 1997, during the height of Southeast Asia’s worst-ever air-pollution crisis.

In neighboring Malaysia, hazy conditions also reached “unhealthy” levels, such as in Malacca, where the country’s Air Pollutant Index rose as high as 161 on Saturday. The current bout of smog is Malaysia’s worst since 2005, when deteriorating air-quality levels forced authorities to declare a state of emergency in two areas and briefly close its largest port.

“The haze situation in Malaysia is going to worsen in the coming days with winds carrying smoke from hot spots in Sumatra,” Malaysian Prime Minister Najib Razak wrote Monday on his Facebook page. “Please reduce outdoor activity and drink a lot of water during this period.”

Singapore’s National Environment Agency meanwhile “has been in touch with the Indonesian authorities to register our concern, and renew our offer of assistance [to deal with the fires],” the city-state’s Environment Minister, Vivian Balakrishnan, wrote Monday on his Facebook page.

The Singaporean agency said Monday the recent bout of haze was due to “drier weather conditions” that have resulted in “an escalation in hotspot activities mainly over central Sumatra,” with as many as 138 “hotspots” indicating fires detected Sunday. It advised residents—particularly children, the elderly and those with heart or lung diseases—to cut back on strenuous and prolonged outdoor activity.

Singapore’s air quality remained “unhealthy” as of 1 p.m. local time Tuesday, with a three-hour PSI reading of 104. In Malaysia, authorities say API readings in four areas in the southern state of Johor remain in the “unhealthy” range as of 11 a.m. local time Tuesday, including the Pasir Gudang district with a reading of 153.

According to Singaporean and Malaysian officials, PSI and API readings within the 101 to 200 range indicate “unhealthy” air conditions, while measurements between 201 and 300 represent a “very unhealthy” status. Readings above 300 indicate “hazardous” air quality.

Such haze is a recurring problem for Singapore and Malaysia since the 1980s, as prevailing winds blow over smoke from the burning of forest and peat in Sumatra, the largest island wholly governed by Indonesia.

The region’s worst air-quality crisis occurred in September 1997, when Singapore’s three-hour PSI spiked to an all-time high of 226, thanks to Indonesian forest fires that were set as a cheap but illegal way to clear land for plantations. The burning triggered widespread anger in Southeast Asia, and caused billions of dollars in losses from canceled flights, health problems and lost tourism revenue.

While subsistence farmers and accidental causes have also been blamed, academics say most fires have been detected in plantation areas owned or to be used by palm oil companies—including some based in Singapore and Malaysia.

Some major Singapore-listed palm oil producers with Indonesian operations have denied using fire for land development. Responding to queries from The Wall Street Journal, spokespeople for Wilmar International Ltd. and Golden Agri-Resources Ltd. said Tuesday that their companies impose a strict “zero burning” policy and use only mechanical means to clear land.

“For too long, commercial interests in Indonesia have been allowed to override environmental concerns,” Mr. Balakrishnan said Monday, adding that he would speak to his Indonesian counterpart “personally to convey the seriousness of the situation.”

“This is a recurring problem that we still haven’t been able to stop from happening again, but we will continue to educate the traditional farmers to stop the (slash and burn) practice,” Indonesian Forestry Ministry spokesman Sumarto Suharno said.

“The local authorities, with help from local communities, have taken steps to put out the fire and prevent it from spreading,” Mr. Sumarto said. “Hopefully, it won’t be as bad as last year because of the expected wet dry season this year.”

–I Made Sentana in Jakarta, Abhrajit Gangopadhyay and Celine Fernandez in Kuala Lumpur, and Gaurav Raghuvanshi in Singapore contributed to this article.