The two leaders confirmed in phone talks on Wednesday night there would be "no meaningful dialogue" unless North Korea agreed on "complete, verifiable and irreversible denuclearization," the ministry said in its statement.
"Dialogue for the sake of dialogue would be meaningless," Abe told reporters after the phone talks.
South Korea says its president, Moon Jae-in, who has been pushing for a diplomatic solution to the North Korea standoff, was offered a meeting with North Korean leader Kim Jong Un in Pyongyang. The offer was made via Kim's sister, who visited South Korea last week for the Winter Olympics.
U.S. Vice President Mike Pence, who was also in South Korea for the Olympics opening, said on Wednesday the United States was open to talks with Pyongyang but only to convey that it must give up its nuclear weapons.
Separately, Japan reported what it said it had identified as another suspected illegal ship-to-ship transfer involving a U.N. blacklisted vessel.