A bipartisan group of six senators has reached an "agreement in principle" on immigration including the Deferred Action for Childhood Arrivals program, according to a joint statement released Thursday.

"President Trump called on Congress to solve the DACA challenge. We have been working for four months and have reached an agreement in principle that addresses border security, the diversity visa lottery, chain migration/family reunification, and the Dream Act—the areas outlined by the president. We are now working to build support for that deal in Congress," said the joint statement released by Sens. Lindsey Graham, R-South Carolina; Dick Durbin, D-Illinois; Jeff Flake, R-Arizona; Michael Bennet, D-Colorado; and Bob Menendez, D-New Jersey.

It's unclear if the agreement includes any border wall funding, which Mr. Trump has most recently said needs to be a part of any immigration deal he will sign. Graham and a handful of other members met with Mr. Trump on immigration earlier this afternoon, and by the time the White House briefing was taking place earlier in the afternoon, press secretary Sarah Huckabee Sanders said there was no deal.

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But the agreement doesn't necessarily have support of the GOP leadership. Senate Majority Whip John Cornyn, R-Texas, said he hasn't even seen the agreement.

At a meeting on immigration the president held with a handful of members of Congress earlier in the day, Mr. Trump, made clear this is not going be just some agreement among a small handful of people," Cornyn said. "This is going to have to have broader acceptance."

"I haven't seen their agreement," Cornyn added. "And how do six people find the other 94 in the Senate, I don't get that. "

Sen. John Thune, D-South Dakota, also urged caution.

"I would be cautious about saying we've got a deal. I think we have a long way to go," he told reporters.

Earlier in the afternoon, Flake said they didn't want to release the details of the deal "until we talk to more of our colleagues."

Congress must come to some agreement on immigration, with a Jan. 19 deadline for reaching a spending deal quickly approaching and DACA set to expire March 5.

The president's recent comments have generated confusion over just what kind of immigration deal he would sign. Earlier this week, the president said he would be open to a clean DACA bill, but later clarified that any deal has to include funding for a wall.

Asked Wednesday if he would sign an immigration fix without wall funding, the president's response was clear — "No. No."

This is a developing story and will be updated.

CBS News' Alan He and John Nolen contributed to this report.