The Malaysian prime minister Najib Razak has demanded Indonesia take action against companies responsible for illegal forest fires blanketing the region in smoke.
Malaysia has closed most schools for two days over health concerns posed by the haze.
The fires are used to clear land for plantations in Indonesia.
Singapore and large parts of Indonesia itself are also severely affected during the annual burning season.
"Only Indonesia alone can gather evidence and convict the companies concerned," Mr Najib said during a visit to Italy, according to Malaysian state news agency Bernama.
But Indonesia's President Joko Widodo told the BBC last week that it was "not a problem that you can solve quickly".
Indonesian officials have said more than 20,000 people, including troops, have been deployed to fight the fires.
At least five areas in Malaysia on Sunday recorded "very unhealthy" levels of air pollution, with one reporting "hazardous" levels. The haze can cause coughs and lung infections.
"We will not compromise with anything that may bring harm to our children in schools," Malaysian Education Minister Mahdzir Khalid said, according to AFP news agency.
The thick smoke has affected much of the region:
- All Malaysian schools, apart from some in outlying areas, will remain closed on Monday and Tuesday.
- One of the biggest marathons in Kuala Lumpur was cancelled on Sunday because of fears for the health of the 30,000 runners due to take part.
- Singapore cancelled Saturday's events for its leg of the swimming world cup, as the country's Pollutant Standards Index (PSI) climbed towards a high of 242 - rated "very unhealthy".
- The Philippines' weather agency blamed fires on Sumatra, and monsoon winds carrying the smoke north-east, for seven days of haze in Cebu in the central Philippines.
The fires are started illegally, as a way to clear land for plantations on Indonesia's vast Sumatra and Borneo islands.
Peatlands, typically saturated with water, are drained to make way for palm oil and paper plantations, making the partially decayed vegetation, and the forest above, more easily burnable.
Environmental activists Greenpeace have described Indonesian peatlands as "a virtual climate bomb", storing billions of tonnes of carbon - until released by fires.
If current trends continue, the pollution this year will be among the worst recorded, partly thanks to a longer than usual dry season, caused by the El Nino weather system.
In 1997, out-of-control fires broke pollution records, causing an estimated $9bn (£6bn) in environmental damage.
Malaysian farmers have complained of poor yields caused by the obscured skies, and the Singapore government is taking legal action against companies accused of being behind the fires.
Indonesia declined Singapore's offers to help with fire-fighting operations during a meeting in Jakarta on 1 October, saying they could deal with the problem.
Despite this, volunteers from Singapore have been distributing tens of thousands of free face masks in Indonesia.