Just weeks after Congress settled its long-running fight over military assistance to Ukraine, lawmakers have engaged in a new battle over the level of Pentagon spending for next year.

Senator Mitch McConnell, the Kentucky Republican and minority leader, is pressing along with other Republicans for a significant increase in money for the military and to break the longstanding Democratic rule that domestic funding must rise equally with Pentagon spending.

“This is the most dangerous time in the world since the Berlin Wall came down, and the military spending needs to reflect the needs of our country, which clearly argues against having an arbitrary line that doesn’t spend more on defense than domestic,” Mr. McConnell said. “So I certainly do disagree with that, and we’re going to have a vigorous discussion about it.”

Democrats have demanded parity between domestic and military funding in recent years. They argue that social programs are as deserving as defense and should not get shortchanged — or absorb deeper cuts to accommodate more Pentagon spending.

Conservative critics of that approach have long contended that parity skews federal spending priorities.

In last year’s deal to suspend the debt limit and avoid a government default, Democrats and Republicans agreed to cap any domestic and military increases at 1 percent for the coming year — setting overall spending on national defense at about $895 billion. While top Democrats have expressed openness to going above that number, they say it cannot happen without an equivalent increase in domestic spending.