The Trump administration wants to change the immigration rules that allowed a man accused of perpetrating a terrorist attack in Edmonton last month to evade a U.S. deportation order years ago and come to Canada.

The White House also wants to tighten security along the U.S. border with Canada as part of a plan to toughen immigration controls across the country.

One administration official cited the case of Abdulahi Hasan Sharif, 30, Sunday evening as President Donald Trump sent Congress a set of border-security and immigration changes he wants passed.

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Mr. Sharif was arrested in San Diego in July of 2011 and ordered deported to Somalia by a judge later that year. He was then released, failed to report for his deportation and could not be located by U.S. authorities after January, 2012. U.S. authorities have said that Mr. Sharif had no known criminal history at the time.

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Mr. Sharif subsequently arrived in Canada and received refugee status. He now stands accused of stabbing a police officer outside a football game at Commonwealth Stadium on Sept. 30 and running down pedestrians in a truck during a later chase.

The administration official said Sunday that Mr. Sharif was released in 2011 because authorities were having trouble deporting him, as Somalia at the time was not repatriating its citizens. The official said the administration wants to "address" this problem.

In his message to Congress, Mr. Trump called for new rules that would "end the practice of catch-and-release" and give Immigration and Customs Enforcement more power to keep prospective deportees in custody until they are removed from the country. Part of the problem, the President wrote, was a 2001 Supreme Court decision that prevents authorities from detaining people for more than 180 days if there is no imminent prospect for their deportation.

Mr. Trump also called on Congress to "improve infrastructure and security on the northern border." He did not detail what exact improvements he wanted to see. Officials also said the U.S. must work to secure both "northern and southern borders."

The references to border security with Canada are unusual. While Mr. Trump has long highlighted what he believes are border problems, he has tended to focus solely on his country's frontier with Mexico.

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These provisions were just two of many demands outlined by the White House Sunday. They also include building Mr. Trump's long-promised wall on the U.S. border with Mexico, cracking down on "sanctuary cities" that refuse to help round up undocumented immigrants and dealing with undocumented immigrants who arrived as children.