He said in a speech as the summit got under way that his push to make the United States a key player in Asia-Pacific was not some "passing fad."
However, diplomats say strains with longtime ally the Philippines could compound Washington's difficulties in forging a united front with Southeast Asian partners on the geostrategic jostle with Beijing over the South China Sea.
Duterte has bristled repeatedly at criticism over his "war on drugs", which has killed about 2,400 people since he took office two months ago, and on Monday said it would be "rude" for Obama to raise the question of human rights when they met.
Such a conversation, Duterte told reporters, would prompt him to curse at Obama, using a Filipino phrase "putang ina" which can mean "son of a bitch" or "son of a whore".
After Washington called off Tuesday's bilateral meeting between Obama and Duterte in response, the Philippines issued two statements expressing regret.
"President Duterte explained that the press reports that President Obama would 'lecture' him on extrajudicial killings led to his strong comments, which in turn elicited concern," the Philippines government said in one statement.
"He regrets that his remarks to the press have caused much controversy," it added. "He expressed his deep regard and affinity for President Obama and for the enduring partnership between our nations."
The White House had earlier said Obama would not pull any punches on his concerns about human rights abuses in the Philippines, its treaty ally, when meeting Duterte.
Instead of the Duterte meeting, Obama plans to hold talks with South Korean President Park Geun-hye, said Ned Price, spokesman for the White House National Security Council - a meeting where the response to North Korea's latest missile tests is expected to be on the agenda.
A Philippines official who declined to be named said there would be no formal meeting rescheduled in Laos but a short 'pull-aside' conversation between the two presidents was still possible.
Moves to soothe tensions
Obama arrived in the city of Vientiane late on Monday for the first visit by a sitting U.S. president to Laos, where he wants to begin to address the legacy of U.S. bombing during the Vietnam War.
He announced on Tuesday that Washington would provide an additional $90 million over the next three years to help Laos, heavily bombed during the Vietnam War, clear unexploded ordnance, which has killed or wounded more than 20,000 people.
The unusually open tensions between the United States and the Philippines, its former colony, threaten to overshadow the Association of Southeast Asian Nations (ASEAN) and East Asia Summits in Laos from Tuesday to Thursday.
The 10-member ASEAN will also meet leaders of other regional powers: China, Japan, South Korea, Australia, India, Russia and the United States.
Duterte won the presidency in May as he promised to suppress crime and wipe out drugs and drug dealers.
About 900 people linked to drugs have been killed in police operations since July 1 and a further 1,500 have been classed as "deaths under investigation", a term human rights activists in the Philippines say is a euphemism for extrajudicial killings.
Duterte has repeatedly poured scorn on critics, usually larding it with curses.
He lambasted the United Nations after it criticized the surge in killings and he turned down a meeting with U.N. Secretary General Ban Ki-moon at the Laos summit.
In May, he called Pope Francis a "son of a whore", although he later apologized, and called U.S. Ambassador Philip Goldberg a "gay son of a whore".
On Tuesday, Duterte met the leaders of Singapore, Japan and Vietnam.
Manila has been aligned with the United States in its dispute with China over the South China Sea, in which Washington blames Beijing for militarizing a vital global trade route and jeopardizing freedom of movement at sea and in the air.
China rejects those accusations and accuses the United States of ratcheting up tensions unnecessarily. China claims most of the South China Sea, through which more than $5 trillion of trade moves annually. Brunei, Malaysia, the Philippines, Taiwan and Vietnam have rival claims.
An arbitration court in The Hague in July invalidated China's territorial claims after a case was brought by the Philippines, a ruling Beijing refuses to recognize.
Duterte said last month he expected all ASEAN members to support the arbitration court's ruling, but that the Philippines would not raise the issue in Laos.