The order came after the Philippines recalled its ambassador and consuls in Canada last week in response to the expiry of the May 15 deadline it had given Ottawa.
Presidential spokesperson Salvador Panelo said Duterte was "outraged" by Canada's inaction in collecting tonnes of waste that it illegally shipped to the Philippines between 2013 and 2014.
"President Duterte is upset about the inordinate delay by Canada in shipping back its garbage containers. We are extremely disappointed with Canada's neither here nor there pronouncement on the matter," Panelo said.
"Canada is not taking this issue nor our country seriously. The Filipino people are gravely insulted about Canada treating this country as a dump site," he said and added, the President had instructed the appropriate office to look for a private shipping company, which would shift the trash to the Canadian jurisdiction.
Panelo said, "If Canada didn't accept its trash, then "we will leave the same within its territorial waters or 12 nautical miles out to sea from the baseline of any of their country's shores", Efe news reported.
The garbage was initially declared to contain only plastic scraps, but was later found to have non-recyclable plastics, household waste and used adult diapers.
Duterte has issued several ultimatum to the Canadian government to remove the containers with some 2,000 tonnes of garbage in a landfill in the city of Tarlac, north of Manila. In April, he even threatened to declare war on Canada over the issue.
In response, the Canadian government agreed to take back the garbage and bear the transportation costs, although it's yet to take action in this regard.
Over the last few years, the garbage dispute has led to several diplomatic protests in the Philippines. The Canadian government, however, refused to act at the time, alleging the garbage shipment was a private transaction that had not been endorsed by the government.
In 2016, Canada amended its regulations to prevent the dispatch of hazardous waste shipments and a Canadian court issued a resolution ordering the importing firm to re-send the garbage back at its own expense.
( With inputs from IANS )