Osaka had announced its plan to end the 60-year relationship in 2017, after San Francisco accepted the donated memorial to women forced into wartime sex slavery by Japanese forces.
But the city took formal action earlier this week to end the ties, with mayor Hirofumi Yoshimura saying "our relations of trust have been destroyed."
The decision was promptly rejected by San Francisco's newly-elected mayor London Breed, who defended the statue as a tribute to all women who have endured "the horrors of enslavement and sex trafficking."
"One mayor cannot unilaterally end a relationship that exists between the people of our two cities, especially one that has existed for over 60 years," she said in a statement.
But officials in Osaka said the decision would stand.
"We have received mixed reactions from our citizens but a majority of them support the decision," an Osaka official told AFP on Friday.
"We delivered our request through proper procedures, though we have not received any official reply," he added.
"We have no plans to reconsider."
Japan's national government has also stepped in to urge San Francisco to reject the memorial, which bears an inscription referring to "hundreds of thousands of women and girls... sexually enslaved by the Japanese Imperial armed forces in 13 Asian-Pacific countries from 1931 to 1945."
Mainstream historians say up to 200,000 women, mostly from Korea but also other parts of Asia including China, were forced to work in Japanese military brothels during World War II as so-called "comfort women".
Activists have in recent years set up dozens of statues in public venues around the world, many of them in South Korea, in honour of the victims.
The statues have drawn the ire of Tokyo, which has pressed for their removal.
In April, a bronze sculpture symbolising "comfort women" was removed in Manila after Japan voiced its displeasure.