Lisa MacLeod, the provincial minister overseeing the immigration file, said Trudeau's comments were "disrespectful" and argued neither the province nor its municipalities should be on the hook for commitments made by the prime minister.
"The premier asked me a question that a lot of people have asked me: 'Why don't we just stop them at the border?"
"We have to provide due process for people according (to) Canadian law and values", Trudeau said.
Trudeau also criticized conservative politicians - the prime minister didn't name names, though said they're both here and around the world - for making the refugee issue as a divisive one.
"Unfortunately, conservative politicians here and around the world are playing a very unsafe game with something that shouldn't be fodder for division", he said.
Ford didn't speak with the media following Thursday's meeting and declined an invitation to appear on Metro Morning.
Premier Doug Ford, who met with Trudeau on Thursday, said he will not dedicate any provincial resources to people who have crossed the border illegally into Canada from the United States, likely fleeing a clamp-down by President Donald Trump.
On Friday, the Ontario government said it faces a "looming crisis" next month if Ottawa doesn't help find space for refugees and asylum seekers now sheltered in college dorms.
MacLeod added the province will continue to welcome those who immigrate through official ports of entry, and will still provide supports to those people.
She described the August 9 closure of the temporary shelters at Humber College and Centennial College as a "looming crisis", one that the federal government must take responsibility for.
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A statement from Ford's office, meanwhile, said the spike in refugees has resulted in a "housing crisis" and a strain on provincially run services.
Ontario has been promised $11 million by the federal government but Toronto Mayor John Tory has said the city alone needs $64 million to recoup costs.
For example, the CEO of Ontario Power Generation earned almost $1.6 million a year ago, making him the highest-paid public-sector employee in the province on a growing list of those earning $100,000 or more.
"Right now, we are saying we have a problem and we need help", Tory said. Tory said many offered to pitch in.
Monica Boyd, a University of Toronto sociology professor who studies immigration, said the issue has always been a point of conflict between the federal government and the provinces and this is just the latest example.
The federal government has already earmarked C$11m ($8.4m; £6.3m) to help Ontario with housing asylum seekers, but Mr Tory said he needs more like C$64m.
Toronto is now housing some 800 migrants, including 200 children in dormitories at two Toronto colleges - a temporary solution that will end in August when students return to school.
He said the federal government hopes to create an "orderly system" to move refugees out of cities to other places.
"We need Ontario to be part of the solution", he said.