He offered his "profound respect" and "eternal condolences" for US soldiers who died in the conflict.
Mr Abe is on a state visit to the US to discuss a wide-ranging trans-Pacific trade deal.
He and US President Barack Obama have also agreed on new guidelines for defence co-operation.
But his speech to the joint session of Congress was scrutinised for comments on Japan's aggression in World War Two. This year marks the 70th anniversary of the end of the conflict.
Mr Abe said he had visited the World War Two memorial in Washington and reflected upon the 400,000 American troops who died with "deep repentance in my heart".
"My dear friends, on behalf of Japan and the Japanese people, I offer with profound respect my eternal condolences to the souls of all American people that were lost during World War Two,'' he said, to warm applause.
Mr Abe also acknowledged that Japan had "brought suffering to the peoples in Asian countries", adding: "We must not avert our eyes from that."
However, correspondents say he stopped short of offering his own apology for Japan's conduct during the war, which included the sexual enslavement of tens of thousands of Asian women by Japanese troops.
In the audience was Lee Yong-soo, one of thousands of Korean women forced into Japanese military brothels during the war.
She was invited to Congress by Democratic Representative Mike Honda, a strong critic of Mr Abe.
Mr Abe was the first Japanese Prime Minister to address a joint session of the US Congress.
He also urged lawmakers to support the Trans-Pacific Partnership (TPP), "for the sake of our children and our children's children"
The TPP is aimed at liberalising markets in 12 countries and the US and Japan are among the biggest players.
Mr Abe said the deal was about spreading shared values of rule of law, democracy and freedom.
He added: "It is also about our security. Long-term, its strategic value is awesome. We should never forget that.
"Let us bring the TPP to a successful conclusion through our joint leadership."
Japanese Prime Minister Shinzo Abe has expressed "deep repentance" over Japan's role in World War Two, during an historic address to the US Congress.