The threat came as Indonesia faced pressure from its neighbours to douse the blazes, which are blamed for sending air quality plummeting in parts of Southeast Asia.
"I've told the military and police chiefs to sack people who don't tackle forest fires," Widodo told a ministers meeting on the issue in Jakarta.
"We'll be humiliated in front of other countries if we can't solve this haze problem.
"No matter how small the fire is, put it out immediately," he added.
Indonesian authorities are deploying thousands of extra personnel to prevent a repeat of the 2015, fires, which were the worst for two decades and choked the region in haze for weeks.
The blazes are an annual problem during the dry season but they have worsened in recent weeks.
Many of the worst fires occur in carbon-rich peat, which is highly combustible once drained to make way for agricultural plantations.
Widodo said the 2015 fires caused some 221 trillion rupiah ($15.5 billion) in financial losses and burned about 2.6 million hectares (6.4 million acres) of land.
"That should never happen again," Widodo said. Officials from Indonesia, Malaysia, Singapore, Thailand and Brunei discussed the pollution issue at an annual meeting in Brunei which wrapped up Tuesday, Malaysia's environment ministry said.
Malaysia will ask participants to "take pro-active action" to make sure that forest and peat fires in Southeast Asian countries can be controlled to avoid haze, the ministry said in a statement ahead of the gathering.
Malaysia said smog had appeared around Kuala Lumpur and on the west coast of peninsular Malaysia due to fires on Indonesia's Sumatra island and the Indonesian part of Borneo island.
Air quality dipped to unhealthy levels in some parts of Malaysia last week. Conditions were better Tuesday afternoon, with air quality recorded as "moderate" in many places.
Skies over Singapore looked hazy with the environment agency saying that air quality was moderate.
Last week, Indonesia sent almost 6,000 extra personnel from the military, police and disaster agency to fight the blazes while an emergency has been declared in six provinces.
"We're working hard and doing everything we can to stop the fires so it (the haze) will not reach neighbouring countries," Indonesian disaster agency spokesman Agus Wibowo said.