"For what has happened, as President, I say sorry and seek the understanding of our relatives in Singapore and Malaysia," he said.
"Indonesia had no intention to cause this. And we will continue to bear responsibility to overcome what has happened," he said in a televised press conference at his office yesterday.
Singapore's pollution index have hit record levels in the past week, and Malaysia has declared a state of emergency in two areas.
Yudhoyono's comments came as Indonesia stepped up its response to the haze with forest fires in Riau continuing to spread, amid efforts to control them by cloud-seeding and water-bombing, and after some of his ministers had hit out at neighbouring countries' reactions to the haze.
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Yudhoyono said he has ordered an investigation of the fires.
"There should be a thorough investigation. In my analysis, there are both natural and human factors," he said.
The blaze strained diplomatic relations between Indonesia, Malaysia and Singapore last week, as governments argued over who was to blame for the smog, and an Indonesian official suggested that Malaysian and Singaporean companies in Sumatra also bore some responsibility.