The Trump administration faced intensifying pressure on Sunday over its mass immigration crackdown in Minneapolis, after federal agents shot dead a second US citizen and graphic cell phone footage again contradicted officials' immediate description of the incident.

Federal agents on Saturday morning shot and killed Alex Pretti, a 37-year-old ICU nurse, while scuffling with him on an icy roadway in the Midwestern city, less than three weeks after an immigration officer fired on Renee Good, also 37, killing her in her car.

The Trump administration quickly claimed that Pretti had intended to harm the federal agents – as it did after Good's death – pointing to a pistol it said was discovered on him.

However, video shared widely on social media and verified by US media showed Pretti never drawing a weapon, with agents firing around 10 shots at him seconds after he was sprayed in the face with chemical irritant and thrown to the ground.

After top officials described Pretti as an "assassin" who had assaulted the agents, Pretti's parents issued a statement on Saturday condemning the Trump administration's "sickening lies" about their son.

Asked on Sunday what she would say to Pretti's parents, Homeland Security Secretary Kristi Noem said: "Just that I'm grieved for them."

"I truly am. I can't even imagine losing a child," she told Fox News's "The Sunday Briefing."

While continuing to defend the agents' actions, her tone was markedly different from a day earlier, when she repeatedly told a briefing that Pretti had attacked law enforcement and "was there to perpetuate violence."

She said on Sunday that more clarity would come as an investigation into the incident continues.

Deputy Attorney General Todd Blanche, speaking to NBC's "Meet the Press," also said an investigation was necessary to get a full understanding of the killing.

Asked if agents had already removed the pistol from Pretti when they fired on him, Blanche said: "I do not know. And nobody else knows, either. That's why we're doing an investigation."

Their comments came after multiple senators from US President Donald Trump's Republican Party called for a thorough probe into the killing, and for cooperation with local authorities.

"There must be a full joint federal and state investigation," Senator Bill Cassidy of Louisiana said.

The top Democrat in the Senate, Chuck Schumer, said his party would vote against funding legislation that includes money for the Homeland Security Department that oversees ICE, the federal immigration agency.

Congress faces a January 30 deadline to fund the government or risk a partial government shutdown.

Schumer, in a Sunday statement, said Republicans should "join Democrats in overhauling ICE and CBP to protect the public," referring to US Customs and Border Protection.

Moderate Democrats, who broke with their party during last year's government shutdown standoff and have been most cautious to not appear as anti-law enforcement, have joined this call.

“This is clearly not about keeping Americans safe, it’s brutalising US citizens and law-abiding immigrants,” Nevada Senator Catherine Cortez Masto ‍said in a statement about the ICE operation.

The Trump administration controversially excluded local investigators from a probe into Good's killing.

Minnesota's Democratic Governor Tim Walz said on Saturday that the "federal government cannot be trusted to lead this investigation. The state will handle it, period."

The Republican chairman of the House Homeland Security Committee meanwhile requested that top officials testify at public hearings.

Thousands of federal immigration agents have been deployed to heavily Democratic Minneapolis for weeks, after conservative media reported on alleged fraud by Somali immigrants – racially tinged accusations that Trump has repeatedly amplified.

The city, known for its bitterly cold winters, has one of the country's highest concentrations of Somali immigrants.

Since the beginning of "Operation Metro Surge," many residents have begun carrying whistles to notify others of the presence of immigration agents, while sometimes violent skirmishes have broken out between the officers and protesters.

Following the latest killing, Walz and other local officials reiterated their call for the agents to leave immediately.

Local authorities have sued the federal government seeking a court order to suspend the operation, with a first hearing set for Monday.

Late on Saturday, a federal judge ordered the Trump administration not to destroy or alter any evidence from the Pretti killing.

Recent polling has shown voters increasingly upset with Trump's domestic immigration operations, as videos of masked agents seizing people off sidewalks – including children – and dramatic stories of US citizens being detained proliferate.

Barack and Michelle Obama on Sunday forcefully condemned the killing of Pretti, saying in a joint statement it should be a "wake-up call" that core US values "are increasingly under assault."

The former president and first lady blasted Trump and his government as seeming "eager to escalate the situation," demanding they work with Walz and other local officials. (Agencies)