His comments followed a Kyodo news agency report on Sunday that cited officials of Britain, the United States and other countries as saying Japan had decided not to join them in issuing a statement scolding China for the new law, which could endanger Hong Kong's special autonomy and freedoms.
But Tokyo was deeply concerned, Abe told parliament.
"Hong Kong is an extremely important partner in terms of both tight economic ties and human relations, and it is important that the original system of 'one nation, two systems' be upheld and things proceed stably and democratically," he said.
Japan expressed concern about Beijing's move in a statement on May 28, the day China passed the law, and called in the Chinese ambassador to convey its view.
A government source familiar with the matter said Japan did not participate in the joint statement partly because of "rather short notice" and partly in order to focus on efforts by the Group of Seven nations, rather then the signatories.
"Japan took the position to do what it has to do independently, in this case because of, first, time constraints, and secondly, our basic position is that we emphasise our efforts in the G7," the source told Reuters.
Other countries had expressed appreciation for Japan's independent efforts, and it received no complaints, added the source, who sought anonymity because the matter was sensitive.
"We've expressed our opinions this way directly and promptly to China at a high level and have made our opinions quite clear to international society," Yoshihide Suga, the chief cabinet secretary, told a news conference.
Tokyo is in a bind amid the U.S.-China tension over Hong Kong as it plans for a state visit by Chinese President Xi Jinping, originally set for April but postponed over the coronavirus.