The Democrats vying to replace Graham Platner as the party’s Senate nominee in Maine quickly seized on the Monday shooting of a man in Biddeford by a federal immigration agent, with some aiming to tie Senator Susan Collins, the Republican incumbent, to President Trump’s immigration crackdown.

Two of the Democratic candidates, Dr. Nirav Shah and Troy Jackson, rushed to Biddeford to participate in a demonstration against Immigration and Customs Enforcement, with Mr. Jackson joining protesters outside Ms. Collins’s office in the city and vowing to “abolish ICE.”

How the shooting unfolded remained uncertain on Monday evening. State and local officials demanded a full investigation, and the Department of Homeland Security released a statement saying that it had happened as ICE agents sought someone who was in the country illegally, for whom they had a removal order.

But it was unclear whether the man who was killed, who pro-immigrant groups have said was a 26-year-old from Colombia, was the person agents had been seeking in Biddeford, a coastal city south of Portland.

On Monday afternoon, as details emerged about the shooting, Ms. Collins called for a “full and impartial investigation of what happened.”

But as Maine Democrats prepare for a convention in late July where state party delegates will choose a new Senate nominee, several potential challengers to Ms. Collins pointed to her past votes on ICE.

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