Canadian police say the bodies of six people from two families, one Canadian-Romanian and the other Indian, have been found in a swamp near the border with the United States, which they tried to enter illegally.

Lee Anne O'Brien, deputy chief of local police, said the bodies were found on Thursday near a capsized boat owned by a man still missing from the Akwesasni indigenous community.

"The six people appear to belong to two families, one of Canadian Romanian origin and the other of Indian citizenship," she said, adding that among the deceased was a child under 3 years old.

"We believe they were trying to enter the United States illegally from Canada," she said, stressing that they had arrived in Canada legally.

O'Brien said no second child from the Romanian family had been found, while his Canadian passport had been found, and police were continuing their search.

A helicopter and diver teams from various police departments were dispatched to the scene to assist in the search.

Authorities said the weather conditions were very bad, with rain, frost and strong winds, when the "very small" boat tried to cross the border.

Local police said they had recently noticed "an increase in the number of people crossing Akwesasni to enter the United States," with 48 crossings recorded since the start of the year.

Two people have already died this year trying to enter the United States illegally from Canada.

The two countries reached agreement on tackling the growing problem of irregular migration along their borders during US President Joe Biden's visit to Ottawa last week.

The deal provides for the return of undocumented asylum seekers who cross the border to Canada, while Ottawa has committed to taking in more migrants.

The deal has been heavily criticised by migrant rights groups who believe it poses more risks to those trying to cross the border illegally.