But the BBC's Rupert Wingfield-Hayes says that the opposition is expected to launch legal challenges to rule the bills as unconstitutional.
Our correspondent says those in Japan who oppose the bills believe they break Japan's explicitly pacifist constitution and also distrust Mr Abe, who is known for his right-wing nationalist views.
Organisers of a large protest which took place outside parliament on Wednesday night said about 100,000 people showed up.
"I'm angry at both the new security bill and Prime Minister Abe. The bill is against Japan's constitution... Abe does not understand it," student Jinshiro Motoyama told the BBC.
Mr Abe first put the changes in motion last year when he sought to reinterpret Japan's pacifist constitution to allow the bills.
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