WASHINGTON — North and South Korea accelerated their diplomatic confrontation on Tuesday over the recent sinking of a South Korean warship, with the South saying it would redesignate the North its “archenemy” and North Korea severing almost all of its remaining ties to its far wealthier neighbor.

American officials were cautious in their public statements, eager to avoid giving the North reason for further escalation. Military officials said no additional American combat forces, warships or aircraft had moved into the region — a standard practice in many past crises, including one in 2003. Officials watching activity on the ground through satellite photographs said there was no “unusual” activity at North Korea’s main nuclear test site.

Both South Korea and the United States have blamed North Korea for the sinking of the ship, which they say was hit by a torpedo.

The biggest concern within the Obama administration is that the diplomatic skirmishing between the North and South that has followed could spill, by design or accident, into an armed confrontation. The confrontation already appears to be the closest the two countries have come to open hostilities since 1994, when the North threatened to turn Seoul into a “sea of fire” if its nuclear violations were referred to the United Nations for sanctions. South Korea and the United States have said they will bring the issue of the sinking, which killed 46 sailors, to the Security Council for unspecified action.