SEOUL, South Korea — South Korea announced Saturday that it will soon start talks with the Trump administration about allowing Seoul to build more powerful ballistic missiles to counter the North, but current and former American officials said the move would have little effect on the most urgent problem facing Washington: North Korea’s apparent ability to strike California and beyond.

The South’s newly elected president, Moon Jae-in, called for the relaxation of limits on its missile arsenal hours after the North launched an intercontinental ballistic missile, or ICBM, 2,200 miles into space, which landed its warhead just off the coast of Hokkaido, the northernmost Japanese island. Experts quickly calculated that the demonstrated range of that test shot, if flattened out over the Pacific, could easily reach Los Angeles and perhaps as far as Chicago and New York, though its accuracy is in doubt.

The new missiles that South Korea wants, in addition to being able to strike deep into the North, could be a way of pressuring China to restrain Pyongyang because the missiles would probably be able to hit Chinese territory as well.

Mr. Moon’s top national security adviser, Chung Eui-yong, called his White House counterpart, Lt. Gen. H. R. McMaster, early on Saturday Seoul time to propose that the allies immediately start negotiations to permit South Korea to build up its missile capabilities. General McMaster agreed to the proposal, which would probably involve increasing the payload on South Korea’s ballistic missiles, according to officials in both countries.