If Mr. Abe did nominate Mr. Trump, such an act would be in keeping with efforts to curry favor with the president.
Mr. Abe was the first world leader to visit the then-president elect at Trump Tower in New York after his election in November 2016, and has talked by phone or in person with Mr. Trump numerous times, always taking care to avoid any criticism of him.
While serving as host to the president in Tokyo in November 2017, Mr. Abe took the American leader to play golf and gave him a hat emblazoned with the slogan “Donald & Shinzo Make Alliance Even Greater,” in reference to Mr. Trump’s own slogan, “Make America Great Again” and the longstanding alliance between the two nations.
On Twitter, Yuichiro Tamaki, the head of another opposition party, the Democratic Party for the People, questioned the wisdom of nominating Mr. Trump for the peace prize when his diplomacy with Mr. Kim had so far yielded few results.
“Abduction, nuclear and short- to midrange missile issues are not resolved at all,” Mr. Tamaki wrote. “I am concerned that it would give the wrong message to North Korea and the international community if we accept that the current situation deserves the Nobel Peace Prize.”
On a morning news show on the mainstream network TV Asahi, Shiro Tazaki, a journalist, said that perhaps Mr. Abe wanted to remind Mr. Trump that Japan needs American protection from North Korea, and that with little leverage of its own, Tokyo needs Washington’s help to push more for the release of the Japanese abductees.
One of Tokyo’s biggest concerns is that in a summit meeting with Mr. Kim due to take place next week, Mr. Trump might accept a deal in which North Korea agrees to give up intercontinental ballistic missiles but retains short- and medium-range missiles that could reach Japan.
Japan “relies on President Trump for the abduction and security issues,” Mr. Tazaki said. “Prime Minister Abe needs President Trump’s cooperation, so maybe that’s why he might have recommended him for the Peace Prize?”