Over all, Mr. Hagel’s proposal, the officials said, is designed to allow the American military to fulfill President Obama’s national security directives: to defend American territory and the nation’s interests overseas and to deter aggression — and to win decisively if again ordered to war.

“We’re still going to have a very significant-sized Army,” the official said. “But it’s going to be agile. It will be capable. It will be modern. It will be trained.”

Mr. Hagel’s plan would most significantly reshape America’s land forces — active-duty soldiers as well as those in the National Guard and Reserve.

The Army, which took on the brunt of the fighting and the casualties in Afghanistan and Iraq, already was scheduled to drop to 490,000 troops from a post-9/11 peak of 570,000. Under Mr. Hagel’s proposals, the Army would drop over the coming years to between 440,000 and 450,000.

That would be the smallest United States Army since 1940. For years, and especially during the Cold War, the Pentagon argued that it needed a military large enough to fight two wars simultaneously — say, in Europe and Asia. In more recent budget and strategy documents, the military has been ordered to be prepared to decisively win one conflict while holding off an adversary’s aspirations in a second until sufficient forces could be mobilized and redeployed to win there.

The Guard and Reserves, which proved capable in their wartime deployments although costly to train to meet the standards of their full-time counterparts, would face smaller reductions. But the Guard would see its arsenal reshaped.

The Guard’s Apache attack helicopters would be transferred to the active-duty Army, which would transfer its Black Hawk helicopters to the Guard. The rationale is that Guard units have less peacetime need for the bristling array of weapons on the Apache and would put the Black Hawk — a workhorse transport helicopter — to use in domestic disaster relief.