President Donald Trump's border chief, Tom Homan, has vowed to press ahead with the government's mission of “immigration enforcement in Minnesota” after federal agents killed two protesters, telling reporters the president wanted to see the situation "fixed".

"We're going to make sure we do targeted enforcement operations, and I'll repeat it: we are not surrendering our mission at all. We're just doing it smarter," he told a news conference on Thursday.

"President Trump wants this fixed. And I'm going to fix it, with your help," he added.

Trump administration officials are working on a plan to "soon" reduce the number of Immigration and Customs Enforcement (ICE) agents in the twin cities of Minneapolis and St. Paul in Minnesota, Homan said.

Homan acknowledged faults in the administration’s immigration crackdown but said the reduction in the number of ICE officers is contingent on the implementation of agreements with state and local officials.

"The withdrawal of law enforcement resources here is dependent upon cooperation," he said.

"We have some agreements. We've got more to talk about regarding how we're going to implement these agreements. But as we see that cooperation happens, then the redeployment will happen."

Earlier, the Senate Democrats threatened to block legislation that would fund the Department of Homeland Security and several other agencies if Republicans and the White House did not agree to new restrictions on President Trump's surge of immigration enforcement.

Protests against ICE operations and federal shootings have taken place for more than a month in Minneapolis and St. Paul, with demonstrations escalating following the killing of Alex Pretti, a 37-year-old intensive care nurse, by immigration officers on Saturday, and the January 7 killing of Renee Nicole Macklin Good, a 37-year-old mother of three.

The Pretti shooting heightened existing tensions as local and state leaders demand independent investigations and question federal cooperation with authorities.