National Security Council spokesman Ned Price said Mr Obama would meet South Korea’s president instead.
Mr Obama had said he would raise the issue of drug-related extrajudicial killings in the Philippines.
Mr Duterte said if he did that, “Putang ina (son of a whore) I will swear at you in that forum.”
Mr Obama flew to Laos on Monday for an Association of Southeast Asian Nations (Asean) summit, after attending the G20 meeting in Hangzhou, China.
Speaking in Manila before he left for Laos, Mr Duterte referred to his anti-drugs campaign that has led to the killing of 2,400 suspected drug dealers and users since he took office in June.
Mr Duterte has sanctioned the killing of drug dealers to try to wipe out the narcotics trade.
“The campaign against drugs will continue. Many will die, plenty will be killed until the last pusher is out of the streets.
“Until the [last] drug manufacturer is killed we will continue.”
He said Mr Obama must not disrespect him.
“We will be wallowing in the mud like pigs if you do that to me,” he said.
Mr Obama had replied that Mr Duterte was a “colourful guy” and that he had asked his team “to find out, is this in fact a time where we can have some constructive, productive conversations”.
Mr Price later indicated it was not.
“Instead, he will meet with President Park [Geun-hye] of the Republic of Korea this afternoon,” he said.
Mr Obama’s last scheduled trip to Asia as president has not been without incident, having also been caught up in a protocol row with hosts China over his arrival in Hangzhou.
The UN has repeatedly condemned Mr Duterte’s policies as a violation of human rights. The Roman Catholic Church, the dominant religion in the Philippines, has also criticised Mr Duterte.
In August, two UN human rights experts said Mr Duterte’s directive for police and the public to kill suspected drug traffickers amounted to “incitement to violence and killing, a crime under international law”.— BBC