US President Donald Trump has said his immigration crackdown was "too tough", marking one of his clearest public retreats from a defining plank of his political agenda, following his party's drubbing in the midterm elections.

In an interview with CBS' 60 Minutes programme, Trump said he believed he deserved an "A plus" for drastically limiting illegal border crossings, but he had been politically "hurt" by sweeping deportations.

His acknowledgement came despite his homeland security department insisting it was not backing away from the crackdown.

Election day polling indicated immigration was the third most important issue for midterm voters, after the economy and the state of democracy.

In historically conservative states like Texas, a swing of Latino voters towards Democrats helped seal the Democratic Party's landslide majorities in Congress.

The president told 60 Minutes that immigration "both helped and hurt" his fellow Republicans in Tuesday's midterms.

"I think I got an A plus for closing up the border," he said in the programme that aired on Sunday evening.

He added: "For getting people out, I get very high marks for getting the bad ones out.

"But I get hurt because we also took people that had good jobs, that created one violation, or breaking of the law, and that was that they came into the country illegally."

"I think it was too tough," the president said.

Trump also said he'd "love to do something on immigration" with congressional Democrats, without offering details.

In a previous interview with 60 Minutes a year ago, a defiant Trump insisted his administraiton's immigration raids "haven't gone far enough".

His conciliatory words on Sunday were an abrupt change in tone from a White House statement earlier in the day to the BBC.

A spokeswoman vowed "the administration will not slow down its efforts to arrest and deport criminal illegal aliens who terrorise our communities".

The Department of Homeland Security (DHS) also showed no sign of a U-turn on Sunday.

"ICE is NOT backing away or slowing down," a DHS spokesperson told the BBC.

Following Tuesday's electoral losses, Vice-President JD Vance had appeared receptive to adjusting their immigration strategy.

"I'm open to the idea that we should change enforcement - by focusing more on businesses that hire illegal labour, for instance," Vance wrote in a lengthy online post reflecting on the results.

However, Trump's promotion on Friday of immigration hawk Stephen Miller to White House chief of staff signalled no climbdown from the administration.

Miller is widely seen as the architect of the administration's hardline immigration policy during the first and second Trump presidencies.

Immigration and Customs Enforcement (ICE) sources told CBS that in recent weeks officials have been instructed to aim for about 2,700 arrests of illegal immigrants per day, an increase from an earlier 2,000 daily arrest target.

Enforcement sweeps this year spurred anti-ICE demonstrations in cities including Chicago, Minneapolis and Los Angeles.

In Minneapolis, two US protesters, Renee Good and Alex Pretti, were fatally shot by immigration agents. (BBC)