With Prime Minister Shinzo Abe having endorsed at a summit U.S. President Donald Trump's determination to take military action against North Korea if necessary, Japan faces new difficulties in resolving the issue of abductions of its nationals by Pyongyang.

Abe has said rescuing Japanese citizens abducted by North Korea in the 1970s and 1980s is a "top priority" for his Cabinet, but if the military option is taken in response to North Korea's growing nuclear and missile threat, it would inevitably jeopardize the abductees' lives.

The families of the abductees have opposed the use of force against Pyongyang, and while Japanese defense officials are preparing for contingencies, Tokyo continues to hope that North Korea's nuclear ambitions can be tackled without Washington resorting to military action.

Trump ratcheted up pressure on North Korea even before he met Abe, saying before a crowd of U.S. and Japanese troops at the U.S. Yokota Air Base shortly after he arrived Sunday that "no one -- no dictator, no regime and no nation -- should underestimate, ever, American resolve."

At a summit in Tokyo on Monday, Abe voiced support for Trump's "all options are on the table" stance. "We reaffirmed that Japan and the United States are 100 percent together," Abe said at a joint press conference with Trump.

A senior Japanese government official said, "The situation surrounding North Korea is set to escalate further. Japan has no choice but to strengthen cooperation with the United States."

But while Abe also said at the press conference that he remained determined to resolve the abduction issue, a Foreign Ministry official expressed mixed feelings about his policy.

"The possibility cannot be ruled out that a military attack would kill Japanese abductees, given that President Trump has threatened to 'totally destroy' North Korea," the official said.

Even if the United States conducts a limited attack on Pyongyang, the abductees could be executed as political criminals given that Japan is a U.S. ally and that among the leaders of nations friendly to Washington, Abe is seen as the closest to Trump, the official said.

Japanese Vice Foreign Minister Shinsuke Sugiyama told reporters after meeting with U.S. Deputy Secretary of State John Sullivan in Tokyo last month that his ministry will continue trying to resolve issues related to North Korea in a "diplomatic manner."

"We discussed the idea that all options are on the table, but Mr. Sullivan and I, as representatives of diplomatic authorities, focused mainly on how to put diplomatic pressure and how to force North Korea to change its policy by maximizing pressure."

"I think defense authorities may have a different angle, though," Sugiyama added.

Tokyo officially lists 17 citizens as having been abducted by Pyongyang's agents and suspects North Korea's involvement in other disappearances of Japanese citizens. Five of the 17 were repatriated in 2002.

Pyongyang has said eight -- including Megumi Yokota who was abducted by North Korea in 1977 at age 13 and has become a symbol of the abductees' plight -- have died and the other four never entered the nation.

Sakie Yokota, the 81-year-old mother of Megumi, said at a press conference last month that she does not want war, calling on Trump to cooperate with other countries so that all Japanese citizens abducted by North Korea can safely return home.

Abe says tackling the abduction problem is his "life's work."

In 1988, the parents of a university student who went missing in Europe and was believed to have been abducted by Pyongyang visited the office of Abe's father, former Foreign Minister Shintaro Abe.

In September 2002, Abe accompanied then Prime Minister Junichiro Koizumi to North Korea as a deputy chief Cabinet secretary and asked him to take a hardline stance toward the country, which helped draw words of apology for the abductions from the country's then leader, Kim Jong Il.

"Prime Minister Abe has a very strong determination to resolve the abduction issue," said another senior government official, adding he persuaded Trump to mention the abduction of Megumi in his first speech at the U.N. General Assembly meeting in September.

Condemning Pyongyang's human rights record, Trump said in the speech, "We know it kidnapped a sweet 13-year-old Japanese girl from a beach in her own country to enslave her as a language tutor for North Korea's spies."

The U.S. president also said in a speech after meeting with the families of the Japanese abductees in Tokyo on Monday, "We will work with Prime Minister Abe on trying to get them back to their loved ones."

But asked at the press conference later about how to rescue the abductees if war breaks out on the Korean Peninsula, Trump stopped short of giving a clear answer, saying, "We'll see what happens in terms of the ultimate conclusion."

The Foreign Ministry official said, "I don't think the prime minister will abandon Japanese abductees in North Korea," expressing hope that Abe will ultimately urge Trump to refrain from war against Pyongyang.

In May 2014, Japan and North Korea reached an accord in Stockholm on principles for negotiations toward the settlement of their outstanding issues, including the abduction problem. Japan relaxed its sanctions on Pyongyang, which in turn promised a full-scale investigation into the abductions.

North Korea, however, repeatedly postponed reporting the survey results. The country then disbanded its investigation team and suspended the probe after Japan imposed further sanctions in February 2016 in reaction to Pyongyang's nuclear and missile tests.