US President Donald Trump has said he is "fairly close" to finalising a deal with Democrats in Congress on allowing young immigrants to stay in the United States.

"Does anybody really want to throw out good, educated and accomplished young people who have jobs, some serving in the military? Really!" Trump tweeted.

"They have been in our country for many years through no fault of their own - brought in by parents at young age," he said.

Mr Trump was repeating a key Democratic argument in support of allowing young people who arrived illegally in the United States as children to stay.

Mr Trump's predecessor Barack Obama protected the so-called "Dreamers" through his Deferred Action for Childhood Arrivals (DACA) order.

But Mr Trump rescinded that executive order, and urged Congress to craft a legal solution within the next six months.

Mr Trump later told reporters: "I think we are fairly close but we have to get massive border security."

"We are working on a plan for DACA. People want to see that happen," Mr Trump said in response to questions as he headed to storm-ravaged Florida.

"You have 800,000 young people brought here, so we are working on a plan and we will see how it works out," Mr Trump said. "We will see what happens. Something will happen."

Democratic Senate Minority Leader Chuck Schumer and top House Democrat Nancy Pelosi emerged from a meeting with Mr Trump late last night saying they had a "very productive" dinner meeting in which the discussion focused on the Dreamers.

"There was no final deal, but... we agreed that the President would support enshrining DACA protections into law, and encourage the House [of Representatives] and Senate to act," they said.

"What remains to be negotiated are the details of border security, with a mutual goal of finalising all details as soon as possible," they added, saying Democrats would continue to oppose plans for a border wall.

Instead, a draft border security package could include using new technology, drones, air support, sensors and rebuilding roads, the congressional Democrats said.

"The WALL, which is already under construction in the form of new renovation of old and existing fences and walls, will continue to be built," Mr Trump had tweeted, referring to the proposed barrier along the US-Mexico border that was a cornerstone of his election platform.

Some Republicans have reacted angrily to Mr Trump's position on DACA.

"Trump base is blown up, destroyed, irreparable, and disillusioned beyond repair. No promise is credible," wrote Representative Steve King.