Primary Industries Minister Teresa Kok defends the four companies, saying they were among the 'most respected oil palm cultivators'.
Environmentalists say Bursa Malaysia and the Indonesian government must take stern action after Jakarta names four major plantation groups over fires.
The Klang Valley is the worst hit, with 'very unhealthy' air quality at Johan Setia in Klang, Selangor.
Johan Setia in Klang, Selangor remains the only area with a very unhealthy API of 209.
The standard operating procedure is for schools to close once the Air Pollutant Index (API) reading in their respective areas hits 200.
It comes amid a blame game between Indonesia and Malaysia.
Minister Liew Vui Keong says action may also be taken against companies involved in slash and burn farming.
Sekolah Kebangsaan (SK) Johan Setia, SK Jalan Kebun and Sekolah Menengah Kebangsaan Jalan Kebun ordered to close after API readings passed 200.
Envoy says Malaysia only offered to help Indonesia fight its forest fires.
The prime minister declines to comment on Indonesia's claim that the haze in Malaysia is caused by its own forest fires.
The Indonesian government has sent 9,000 military, police and disaster agency personnel to fight flames raging through Sumatra and Borneo.
Surgical and cloth masks are largely inefficient while N95 masks, which are more expensive, must be worn correctly and changed periodically.
Many areas in Kuala Lumpur, Selangor, Negeri Sembilan and Sarawak also continue to record unhealthy API readings.
Environment minister Yeo Bee Yin says hundreds are being deployed in Sumatra and Kalimantan to put out fires, while offenders are being apprehended.
Fredolin Tangang of UKM warns that rising temperatures will trigger peat fires which are hard to put out.
Some 400 schools have been closed in Sarawak, while in Sumatra, some kindergartens will be closed until Friday.
Deputy minister advises those with respiratory diseases to stay home or wear masks when going outside.
These include Shah Alam, Petaling Jaya and Klang.
But data from Asean meteorological centre contradicts the Indonesian claim, and shows prevailing winds blowing smoke haze towards the peninsula.
Environment minister Yeo Bee Yin says the government will exhaust all diplomatic channels to raise the urgency to Indonesia to act on the haze.
The education department says the examination board will also postpone examinations if the API reaches 300.
Former prime minister says "it's not worth it" to go on with exams in Sarawak because of the persistent haze.
With 1,087 hot spots reported in Kalimantan, Deputy Chief Minister Douglas Uggah Embas says state government does not have the power to act.
Major towns in Sarawak recorded unhealthy API readings.