By Ted Barrett and Phil Mattingly, CNN

Top White House officials met with senior Republican senators Wednesday to try to reach an agreement on government spending levels for the next two years, but the session ended without a deal.

"We had serious discussions," said Sen. Richard Shelby, a Republican from Alabama who chairs the Appropriations Committee, as he left the meeting that took place in the Capitol office of Senate Majority Leader Mitch McConnell.

Shelby said the Trump administration and GOP senators "are close to the same page" but not on it yet.

He said the sides would meet again soon and, in the meantime, he would try to gauge whether there might be the necessary Democratic support in the House and Senate for the budget figures that were discussed "in pretty good detail."

The impasse reflects the divisions between the administration, led by Trump and acting White House chief of staff Mick Mulvaney, who want to reduce domestic but not defense spending, and Republicans on the Hill who recognize that the only way to pass spending bills is with the support of congressional Democrats, and they are eager to bolster domestic programs not cut them.

Shelby was asked if the administration is interested in a deal that would lift spending caps for domestic and defense programs or would it prefer the automatic across the board cuts that would take place through sequestration if an agreement isn't reached.

"The White House is having serious discussions with us in the Senate to try to resolve our dilemma about draconian cuts," he said. "We are not there yet."

North Dakota Republican Sen. John Hoeven said the main impasse revolves around funding level for defense and non-defense programs, which he called a "standard" issue between the parties.

"Ideally, we'd get something that the House and Senate -- Republicans and Democrats -- agree to a number and that the White House would accept," said Hoeven, who is on the Appropriations Committee. "And that's what we're trying to do."

As he left the meeting, Mulvaney refused to answer questions. "I'm not going to talk about it," he said.

Treasury Secretary Steve Mnuchin and acting Director of the Office of Management and Budget Russell Vought also attended the meeting.

"We wouldn't reach an agreement without the President being fully onboard," Mnuchin said. "He's fully briefed on all our conversations."

Sen. John Boozman, a Republican from Arkansas who sits on the Appropriations Committee, summed up the state of play: "We're still in the talking stage, trying to figure out a path forward."