President Trump early Thursday morning contradicted top Democratic leaders' claim that they have excluded the border wall from a deal on the Deferred Action for Childhood Arrivals program.

"No deal was made last night on DACA. Massive border security would have to be agreed to in exchange for consent. Would be subject to vote," Trump tweeted.

"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."

But Trump also indicated in other tweets that he supports the Democrats' goal of finding some way, in legislation, to protect illegal immigrants who came to the United States as children.

"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. Plus BIG border security."

Trump met with Senate Minority Leader Chuck Schumer, D-N.Y., and House Minority Leader Nancy Pelosi, D-Calif., at the White House Wednesday night. "[T]opics included tax reform, border security, DACA, infrastructure and trade."

A White House official said the president had a "constructive working dinner" with the top Democratic leaders and administration officials to discuss policy and legislative priorities. "This is a positive step toward the President's strong commitment to bipartisan solutions for the issues most important to all Americans," the official said.

After the working dinner, Schumer and Pelosi claimed they agreed to exclude the border wall from a deal on DACA.

"We had a very productive meeting at the White House with the President," Schumer and Pelosi said in a joint statement. "The discussion focused on DACA. We agreed to enshrine the protections of DACA into law quickly, and to work out a package of border security, excluding the wall, that's acceptable to both sides."

White House press secretary Sarah Sanders responded Thursday, "While DACA and border security were both discussed, excluding the wall was certainly not agreed to."

On his way to Florida Thursday morning, Trump was asked whether he favors "amnesty" for DACA recipients. Trump replied, "The word is DACA."

Trump said the Congress and the administration are "fairly close" to a deal. "[W]e're working on a plan for DACA."

"The wall will come later," he told reporters before leaving for Florida to survey the damage of Hurricane Irma.

Earlier this month, Trump ordered an end to the 2012 Obama-era program that protects young undocumented immigrants from being deported. Trump gave Congress six months to find a way to fix the legislation before the administration starts phasing out its protection to nearly 800,000 DACA recipients.

Recently, White House House director of legislative affairs Marc Short said, "You will see the administration lay out its principles in a broad sense on what we want to see. The president has also made clear that he does believe that we need to ensure border security."