"I brought that up to the president... and talked about how draconian it would be on defense, and a lot of other issues, but mainly national security and it would set us back in a troubled world in a lot of ways and it would be the wrong signal to the world if we had sequestration," Shelby told reporters.

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The meeting between Shelby, Trump and other administration officials comes a day before congressional leadership is set to meet with Mulvaney and Mnuchin to discuss a budget deal and raising the debt ceiling.

Lawmakers are voicing growing concerns about their ability to get a budget caps deal and avoid another government shutdown starting in October, after the 35-day partial shutdown earlier this year.

"I basically said it's not in my interest, it's not in the American people's interest. …We live in a troubled world. I said we cut defense like that, it sends the wrong message to the world," Shelby said recounting his pitch to Trump.

Asked if Trump understood that he would have to increase non-defense spending in order to get an increase in defense spending, Shelby said that Trump wasn't specifically asked that that but predicted that was a "given."

"I can't say what he ... opposes or what he's for, philosophically. We're all for trying to rein in spending, but at what costs? And I don't think the president wants to rein in spending at the cost of national security," Shelby told reporters, asked if Trump was opposed to sequestration.

He added that he specifically asked for Mulvaney to be in the meeting. Mulvaney, who is viewed as having significant influence on Trump, pushed for steep spending cuts during his time as a member of Congress.

"He's in a powerful position with the president. I think he needed to be in there. Maybe he was going to be there anyway, I don't know, but I wanted to make sure he was there," Shelby said.

He added that Mulvaney mainly "listened" during the meeting, which he described as being positive overall.

"I thought it was a positive meeting," Shelby said. "I've been in a lot of meetings that weren't positive."