The meeting came after U.S. Secretary of State Rex Tillerson said Tuesday that Washington was ready to have direct talks with North Korea without preconditions.
The issue of abductions to North Korea is a highly-charged one in Japan, which suspects dozens of people were kidnapped by agents from the isolated country.
"Unity of the Security Council is crucial on this", he said, adding that it is also important to allow for diplomatic engagement toward a peaceful resolution.
While Japan's alert system succeeded in informing the public about the launches, just 5.6 percent of respondents said they took shelter after North Korea fired on September 15.
Secretary General Antonio Guterres warned against "sleepwalking" into a new war on the Korean peninsula. Feltman's visit was made upon North Korea's invitation.
Hope for dialogue to defuse tension over North Korea's weapons was kindled last week when United Nations political affairs chief Jeffrey Feltman made a rare visit there, the highest level engagement by a United Nations official with North Korea since 2012. "I think for the first 30 minutes the players were a little bit nervous".
"It is very clear that security council resolutions need to be fully implemented", Guterres explained.
"We fully agreed that the denuclearisation of the Korean peninsula is indispensable for the peace and stability of the region", Abe said.
Asked if he is considering a trip to North Korea to meet with leader Kim Jong Un, Guterres said: "Meetings only make sense if there is a goal to those meetings".
Japan says now is the time to keep up maximum pressure on Pyongyang, not start talks on theNorth's missile and nuclear programmes.
After meeting with Prime Minister Abe, Guterres also paid tribute to the Japanese citizens who were forcibly abducted by North Korean agents in the 1970s and 1980s, promising to make his best efforts to bring them home.