The government of Canada is investigating reports that U.S. Border Patrol agents stopped Canadian fishing boats in a search for illegal immigrants in disputed waters off the coast of Maine that Canada has considers its own.

Laurence Cook of the Grand Manan Fishermen's Association said in a personal posting on Facebook that, in a June 24 boat check off the Machias Seal Island "gray zone" in late June, Border Patrol agents claimed "to be looking for illegal immigrants ..."

"Typical American bullies," he wrote.

The fishermen's association confirmed on Facebook that "a few Grand Manan Fisherman were approached" by Border Patrol agents in June.

The Canadian Broadcasting Corp. reported that there have been at least two such stops, and as many as 10 in recent weeks. Amy Mills, spokeswoman for Global Affairs Canada, the nation's diplomatic and consular agency, told NBC News via email that it was looking into the matter.

"Canada continues to investigate these incidents that occurred in Canadian waters, including through engaging with U.S. agencies involved in the matter," she said. "Canada's sovereignty over the Machias Seal Island and the surrounding waters is long standing and has a strong foundation in international law. Until the matter of the boundary is resolved, we will continue to take practical steps with the U.S. to ensure that the area is well‎ managed."

A spokeswoman for U.S. Customs and Border Protection, which oversees the Border Patrol, confirmed the encounters but said they were routine and suggested that agents did not board the boats but rather adjoined them so agents could ask questions.

“U.S. Border Patrol was conducting regular patrol [operations] to enforce immigration laws and other violations of federal law that they may encounter in the course of their duties," she said via email. "... Border Patrol does not board Canadian Vessels in the Gray Zone without consent or probable cause and only conduct interviews as a vessel runs parallel to it, bow to stern."

She referred further questions to the U.S. State Department, which had no immediate response.

Only about 100,000 of the United States' 11.1 million immigrants in the country illegally were from Canada, according to the Pew Research Center in 2014.

The maritime boat checks come amid some of the most strained relations between the United States and Canada in decades. President Donald Trump's duties on Canadian steel and aluminum, announced in May, were met with in-kind tariffs on billions of dollars worth of American goods.

The trade dispute started in earnest after Trump tweeted that Canadian Prime Minister Justin Trudeau was acting "meek and mild" and was being dishonest about Canada's trade barriers during the Group of 7 summit last month in Charlevoix, Quebec.