Environmentalists have urged Indonesian authorities to make good on their promises to get serious about the burning-off.
So far, much of the haze seems to be coming from the Indonesian province of West Kalimantan, on the island of Borneo.
Indonesia-based conservation scientist Erik Meijaard, with the group Borneo Futures, said he was not seeing much effort to extinguish the fires but was hopeful Indonesia would act more quickly.
"West Kalimantan is again on fire quite badly — there's a few hundred fires at least throughout the province," he said.
"Clearly the seriousness of the political message hasn't filtered through to the ground and there's a laissez-faire approach, as there has always been."
Dr Meijaard said the fires were being lit in farmland by smallholders.
They do not appear to have been lit in reclaimed peat land or by palm oil companies.
Disaster Management Agency 'confident' fires will not escalate
Indonesia's National Disaster Management Agency insisted the fires were under control.
"We are confident that it will not escalate widely, because we're keeping up the effort to fight the fires," spokesman Sutopo Purwo Nugroho said.
"We've sent eight helicopters and two water-bombing planes, and also two planes for rain making.
"This will be done continuously until the peak dry season in September."
Mr Sutopo said satellites had picked up a relatively small number of hotspots.
"The source of the haze is from the burning in the farming lands, where people doing burning to clear the land," he said.
"These are not peat lands, and that explains why the smoke is thin."
Dr Meijaard said Indonesia had been lucky with the weather and wind direction so far.
"At the moment the smoke and haze from West Kalimantan is blowing into the South China Sea," he said.
"If Sumatra is now kicking in, in terms of fires, I'm convinced Singapore and Malaysia will be covered in haze in the very near future."
Last year's haze lasted for three months and caused respiratory problems for millions of people, before wet season rains finally extinguished the fires.