Indonesia on Tuesday deployed an extra 1,600 military personnel to fight forest and agricultural fires producing thick haze, as the smog closed schools in Malaysia and worsened air quality in Singapore.

President Joko Widodo ordered the military ramp-up on Sumatra after authorities declared a state of emergency in the island's hard-hit Riau province Monday.

One thousand military personnel were dispatched to Riau while 600 were sent to South Sumatra province to help local authorities fight fires, Indonesia's disaster agency said. They join over 1,000 soldiers sent to Sumatra last week.

Smog-belching blazes, an annual problem in Southeast Asia, have intensified in Sumatra and the Indonesian part of Borneo island in the past two weeks, sending a cloud of acrid smog across the region.

The illegal fires are set to clear vast tracts of land to make way for palm oil and pulp and paper plantations, and Indonesia has failed to halt the practice despite years of pressure from its neighbours.

After announcing late Monday that more troops would be sent to Sumatra, Widodo said he had ordered law enforcement agencies to "take firm legal action against parties responsible for the forest fires".

Around 100 people and 15 companies are being investigated over the blazes, according to the disaster agency.

Tens of thousands of people in smoke-choked regions of Sumatra and Borneo have fallen ill, while air travel there -- as well as in parts of Malaysia -- has been hit by sporadic flight delays or cancellations due to poor visibility.

Malaysia's education ministry ordered schools closed in Kuala Lumpur, three adjacent states and the nearby administrative capital of Putrajaya, as the capital was enveloped in a smoky grey shroud.

Air pollution indices in the affected areas were in the upper range of "unhealthy" and nearing "very unhealthy".

More than half of the country's 52 monitoring stations registered "unhealthy" air on Tuesday.

Malaysian authorities in several areas have distributed free face masks, while the marine and aviation sectors have been advised to go on high alert due to the worsening visibility.

Authorities advised people with respiratory conditions to wear face masks outdoors and for all citizens to limit unnecessary outdoor activity.

The air quality index in Singapore, where fears are mounting that the haze could affect this weekend's Grand Prix, remained in the "unhealthy" range Tuesday.

A heavy downpour brought some relief although the strong smell of burning wood and foliage remained in the air.

Pressure to stop the annual outbreaks of smog has increased since 2013 when Southeast Asia suffered its worst air pollution crisis for more than a decade, but attempts to find a regional solution have moved slowly.