Relatives of Japanese nationals abducted by North Korea decades ago said Sunday a third meeting between U.S. President Donald Trump and North Korean leader Kim Jong Un had revived their hopes for resolving the issue of their missing family members.

Trump and Kim met in the Demilitarized Zone dividing the two Koreas and agreed to restart denuclearization talks within weeks after the rupture of their February summit, held in Hanoi, disappointed many of the relatives.

"I first felt like it was kind of a performance" Kenichi Ichikawa said, referring to the two leaders walking across the border in the zone ahead of their summit.

His younger brother, Shuichi, disappeared from a beach in Kagoshima Prefecture in 1978.

But "I would appreciate it if (their meeting) leads to progress on the abduction issue."

Sakie Yokota, the 83-year-old mother of Megumi Yokota who disappeared on the way home from school in 1977 at the age of 13, said she is not sure if the abduction issue is moving toward a settlement.

"But I hope progress will be made on the issue," she said.

Akihiro Arimoto, 90, who is waiting for the return of his daughter, Keiko, said the United States may help the abduction issue to be settled, just as it suddenly set up Sunday's unplanned meeting.

In late May, Trump met with some family members of Japanese nationals abducted by North Korean agents in the 1970s and 1980s. He vowed to cooperate with Prime Minister Shinzo Abe to secure their return. Arimoto received a hand-written letter from Trump earlier this month.

"It is Japan's turn now (to meet Kim). Prime Minister (Shinzo) Abe should swiftly hold talks with North Korea," he said.