Abe, in a speech marking the 70th anniversary of the war's end, gave no new apology. But he acknowledged previous ones and said Japan must keep resolving to never again use force to settle international disputes.
"Japan has repeatedly expressed the feelings of deep remorse and heartfelt apology for its actions during the war," Abe said, adding the country "engraved in our hearts" the suffering of Japan's Asian neighbors through its actions, including China, South Korea, Indonesia and the Philippines.
But, Abe said, postwar generations now exceed 80% of Japan's population.
"We must not let our children, grandchildren, and even further generations to come, who have nothing to do with that war, be predestined to apologize," Abe said at his official residence in Tokyo.
"Still, even so, we Japanese, across generations, must squarely face the history of the past. We have the responsibility to inherit the past, in all humbleness, and pass it on to the future."
Japan's government has made repeated apologies over the decades, with some prime ministers personally expressing regrets for Japan's actions in the war, including for using women from Korea, China and elsewhere in Asia as "comfort women," or sex slaves, for the Japanese military.
The lack of an apology on Friday drew some tepid to irritated reactions from Japan's Asian neighbors, including China, which Japan had invaded and occupied.
The statement "was a diluted one at best, thus marking only a crippled start to build trust among its neighbors," a column published Friday by China's state-run Xinhua news agency reads.
"Instead of offering an unambiguous apology, Abe's statement is rife with rhetorical twists ... dead giveaways of his deep-rooted historical revisionism, which has haunted Japan's neighborhood relations," the Xinhua article says.
In South Korea, the spokesman for the country's ruling party noted that Abe's statement "did not include a direct apology."
"It's regrettable that he (Abe) mentioned the comfort women issue in a rather indirect way," Kim Young-woo said. "Instead of pinpointing his ambiguous words, we'll continue to urge Japan to show sincere remorse and action for peace."
Abe hinted at the comfort women issue Friday, saying Japan needed to remember the "women behind the battlefields whose honor and dignity were severely injured." He said Japan will help make this century one in which "women's human rights are not infringed upon."
Japan helped establish the Asian Women's Fund in 1995, which is supported by government funds and provides assistance to former comfort women. But Tokyo has resisted direct compensation to the victims, prompting activists and former comfort women to say Japanese leaders are avoiding officially acknowledging what happened.
Only a few dozen of the women are still alive today.
Kim, the South Korean ruling party spokesman, conceded that Abe mentioned remorse and "how Japan caused suffering and pain to innocent people."
"We can see Abe's complex and sad heart," Kim said.
South Korea's foreign ministry told CNN the government was reviewing Abe's statement.
The reaction by North Korea's government, through its official news outlet KCNA, was more pointed.
"Japan is talking about future and responsibility and contribution in the international community without making an apology," North Korea's Foreign Ministry said through KCNA. "It is an unpardonable mockery of the Korean people and an act of deceiving the international community."
Complicating matters for Japan's neighbors is the island nation's apparently shifting military stance.
Japan has had a pacifist stance after the war, deploying troops only in humanitarian roles.
While Abe on Friday distanced Japan from wars of aggression, he has backed legislation that would allow for a more active role for Japanese troops overseas, including involvement in the defense of its allies. China and South Korea, invoking Japan's expansionist past, have expressed concern about the legislation.
Abe, 60, became Japan's first Prime Minister born after the end of World War II when he began a one-year term in 2006. His second stint in the office started in late 2012.