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 federal immigration agents, 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.”

Federal authorities had yet to provide information about the shooting as of Monday evening, but the state attorney general said that an ICE agent had killed a man during an operation in Biddeford, a coastal city south of Portland. The man who was killed, who pro-immigrant groups have said was a 26-year-old from Colombia, “attempted to flee in a vehicle in the direction of the officer and was fatally shot,” the attorney general, Aaron M. Frey, said.

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.

As the chairwoman of the Senate committee overseeing government spending, Ms. Collins this year advanced a bill that would have included money for body cameras and de-escalation training for immigration enforcement officers. But after Democrats would not vote to fund ICE and Customs and Border Protection, Ms. Collins later voted with Republicans to give both agencies $70 billion through a special congressional budget procedure that did not allow Congress to impose those guardrails on immigration agents.

Democratic candidates have pointed to that vote to argue that Ms. Collins handed immigration officers a blank check.

One Senate hopeful, Jordan Wood, a onetime chief of staff to former Representative Katie Porter of California, demanded that Ms. Collins “have the courage to stop funding this lawless agency that’s been terrorizing our streets for over a year.”

“ICE is dangerously out of control and an embarrassment to our country. Abolish it and replace it with an agency that answers to the people,” he wrote on X.

Other Senate candidates used the moment to try to define their policy positions on immigration. With Mr. Platner dropping out last week after a rape allegation, the Maine race has been upended, and many of the new Democratic contenders have yet to publish platforms for federal office.

One Democratic candidate, Shenna Bellows, the Maine secretary of state, wrote on X, “It’s time to get ICE off our streets.”

Dan Kleban, a brewery owner running for Senate, emphasized his moderate commitment to rein in the immigration agency without abolishing it.

In an interview on Monday evening at the brewery he co-founded, Mr. Kleban said that “we need Border Patrol” and “we need safe borders” but that he would not fund ICE without new restrictions.

Biddeford is “thousands of miles away from the southern border,” he said. “This is not about border enforcement. This is about intimidation.”

Then he headed to a vigil in Biddeford for the man who was killed.

At a hastily organized protest earlier in Biddeford, Mr. Jackson and Dr. Shah worked the crowd. One woman grabbed Dr. Shah’s hands and urged him to ensure the victim’s name was heard “across the country.”

“Exactly,” he responded, lamenting “the fact that we don’t remember these names and let them waste from our memory.”

Dr. Shah is viewed as more moderate on ICE than Mr. Jackson, prompting some demonstrators to accuse him of political posturing as he walked through the crowd.

“As the son of immigrants, issues like this are extremely important to me,” Dr. Shah, whose parents came to the U.S. from India, hit back. He left the rally early to outline his policy positions at a news conference in Freeport, about 30 miles north of Biddeford.

There, he said ICE “should be broken down, dismantled, and built back up in a new way that actually respects the rule of law, targets those who are actual threats to this country, and avoids demonizing and — as we saw today — killing someone who is a newcomer to the United States.”

He also took jabs at Ms. Collins, saying she had “erred” in voting to fund ICE this year and drawing a connection between the shooting and “the failures of our current leadership in Washington.”

For his part, Mr. Jackson, the former president of the State Senate, marched to Ms. Collins’s office and City Hall in Biddeford with the protesters.

Speaking of ICE, he told reporters, “We certainly don’t have to give them $70 billion to go around doing what they did here today and what they’ve done in Minnesota.”

“You don’t get a free pass because you say you’re law enforcement,” he added. “And that’s why it’s so important that whoever gets a seat is someone that actually is going to abolish ICE.”

Michael Gold contributed reporting from Washington.