BRUSSELS—The European Union is crafting proposals for stepped-up defense cooperation that could eventually lead to the creation of a small crisis-response force to react—without American help—to a range of security challenges, from conflict in Africa to a major humanitarian disaster.

The European Union’s chief executive is set to make a fresh push Wednesday for bolstering Europe’s defense industry, according to EU officials. He will say EU governments could save more than €25 billion ($28 billion) a year if they better pool and coordinate their defense purchases to focus on the bloc’s overall security needs.

The proposals are part of a broader movement to ratchet up the bloc’s security and defense ambitions. If brought to fruition, they could strengthen a fractured European defense industry and spur the creation of a modest, yet autonomous, European military capability.

The plans, officials say, aren’t aimed at creating a standing EU army, an idea that appeals to some federalists but is deeply divisive in the bloc. Still, they could have far-reaching consequences for the defense relationship between Europe and the U.S. over the next decade.

The proposals, even in their current, nascent stage, remain controversial. Some Eastern European officials are wary, arguing that any EU foray into defense will undermine the North Atlantic Treaty Organization. Others doubt Europe’s capacity to make the plans work.