He said then that the Army should hire 50,000 soldiers to get back to 540,000, and he supports a Navy plan to increase its fleet to 355 ships from 276. That plan calls for the Navy to buy more destroyers and start building three nuclear-powered attack submarines a year instead of two.

But Mr. Trump has also called for a more isolationist foreign policy and has said that American allies should pick up more of the bill for defending themselves. And even central tenets of military strategy are in question. At the same time Mr. Trump has been criticized by lawmakers from both parties for cozying up to Russia, his defense secretary, James Mattis, a retired Marine general, has described that country as America’s “principal threat.”

As a result, independent analysts said, it is hard to square the president’s foreign and defense policies or know what his final priorities would be if Congress only approved part of the money he is seeking.

“It is not clear to me why we would need 355 ships if our foreign policy says we are going to reduce our commitments around the world and let allies do more for their own defense,” said Todd Harrison, a military budget expert at the Center for Strategic and International Studies, a bipartisan Washington research group.

“And if you want to build a military more suited to deter Russia and China than to deter terrorists, it is a very different capability that you want to buy,” Mr. Harrison said. “That is something that the Trump administration has not really rationalized yet.”

Mr. Obama approved a series of sophisticated new weapons projects, including a new long-range bomber for the Air Force and massive ballistic missile submarines for the Navy. So the debate within the Pentagon now is not so much about pitting the services against one another to see whose pet project will survive as it is about determining how much money is needed to keep all the big projects going.

The Air Force, for instance, has been trying to expand production of the F-35 while also building new aerial-refueling tankers, modernizing nuclear missile systems and building the new stealth bombers.