In this case, Mr. Abe and President Park Geun-hye of South Korea have barely been on speaking terms since coming to power just over a year ago. Their antagonism is complex and deeply personal, rooted in World War II history as well as their own conservative and nationalist political leanings, which make old animosities even harder to overcome.

Image Prime Minister Shinzo Abe of Japan at a news conference on sales taxes in Tokyo last year. Credit... Toru Hanai/Reuters

The feud has been a growing source of anxiety for the White House, not the least because of worries that China could use the ill will to drive a wedge between America’s two key allies in Asia. That would give China a freer hand in the East China Sea. Divided, Japan and South Korea are also less effective in pressuring North Korea over its nuclear program.

Vice President Joseph R. Biden Jr. attempted to repair the breach in a visit to Japan and South Korea in December, urging both Mr. Abe and Ms. Park to avoid actions and statements that would inflame the tensions.

But Mr. Abe ignored Mr. Biden’s suggestion not to visit the Yasukuni Shrine, a memorial to the Japanese war dead that has become a loaded symbol to Koreans and Chinese because it also honors people who are war criminals. Mr. Abe’s visit, on the first anniversary of his government, Dec. 26, plunged relations with Seoul into an even deeper freeze.

Convinced the two were not going to mend relations on their own, the White House proposed a “trilateral” meeting with Mr. Obama at the nuclear security summit in the Netherlands. The European locale and nonproliferation theme made sense. “It’s a multilateral meeting not in Asia,” said a senior administration official, “and a multilateral meeting about the one thing Japan and South Korea are in agreement on.”