Defense Secretary Jim Mattis has privately agreed with Capitol Hill defense hawks who say President Trump's budget proposal is not enough to rebuild the military, CNN reported Friday.

Mattis publicly supported Trump's proposed $603-billion defense budget for 2018 but he told lawmakers in recent closed-door meetings that the Pentagon had sought higher spending levels as part of its effort to add troops and upgrade aging equipment, anonymous sources told the news channel.

Trump has said his budget proposal will fund a historic military buildup, including a 350-ship Navy.

"Our military is building and is rapidly becoming stronger than ever before. Frankly, we have no choice!" the president tweeted on Sunday.

But the military is for now still operating under funding levels set during the last year of the Obama administration. Congress is beginning work on the coming year's defense budget in earnest and will weigh the president's proposed budget.

The two Republican chairmen of Congress' armed services committees, Sen. John McCain of Arizona and Rep. Mac Thornberry of Texas, are pressing for a $640-billion base defense spending for 2018 to reverse what they say are years of belt-tightening.

Both have said publicly that the Trump administration proposal is not enough to cover Defense Department needs.