The Trump administration tried to stop federal funding to local authorities in cities such as New York, Los Angeles and Chicago, that decline to hand over undocumented immigrants to the federal government.
The protest was coordinated and organised by the Muslim Community Network and the Yemeni American Community.
The suspect reportedly rented an apartment near the community centre where the shooting took place.
Police named the suspect as Alexandre Bissonnette, a 27-year-old university student. He was charged with six counts of first-degree murder and five counts of attempted murder.
The president-elect is also preparing to meet US intelligence officials to discuss the alleged Russian interference in the presidential election.
The White House suggests that Russian President Vladimir Putin personally authorised cyber attacks during the November poll.
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