Under the deal, South Korea promised not to raise the issue again and Japan transferred 1 billion yen (now $8.9 million) to a foundation dedicated to supporting the victims.
Abe told reporters that the trip will further expand Japan's diplomacy.
Despite a recent cooling of tensions in the run-up to the Winter Olympics in South Korea, Shinzo Abe has insisted on "maximising pressure" on Pyongyang over its nuclear and missile programmes.
The dispute is expected to carry on till next week, when the foreign ministers of both countries will meet in Vancouver, Canada, for a special global summit on the situation with North Korea.
The two countries signed the deal on December 28, 2015, to "finally and irreversibly" settle the comfort women issue, which has always been a key source of tension between the two countries. Instead, the government would not use Japan's funds - a key result of the 2015 deal - and would use its own money to support the victims. Japan's Chief Cabinet Secretary Yoshihide Suga said his participation in the games would depend on his parliamentary schedule.
The re-emergence of a long-simmering issue has poured cold water over improving bilateral ties, as the two United States allies seek closer cooperation to cope with regional security threats such as North Korea.
Representatives of 31 Japanese trading, auto parts, logistics and other companies are accompanying Abe, with the aim of tapping into the stable economic growth and relatively cheap labor costs in the Baltic and Southeast Europe regions, according to Foreign Ministry officials.
The so-called "comfort women" issue involved soldiers from the Imperial Japanese Army (IJA) during World War II, forcibly coercing and even kidnapping girls, some of them underage, and women, and forcing them to work as sex slaves, servicing Japanese soldiers at military brothels during the war.
And while Mr Moon wants to forge "forward-oriented ties" with Japan - separate from the comfort women issue - Dr Minohara said: "This is like punching someone in the face and then saying to them, "I hope it doesn't ruin our relationship".