Reeves vehemently denies ever having met the woman.
The woman is seeking 3 million Canadian dollars ($2.8 million) a month in spousal support, retroactive to November 2006. She also wants $150,000 ($144,000) a month in child support, going back to June 1988.
Karen Sala disputed the DNA results in court Thursday, suggesting they had been tampered with or that Reeves used hypnosis to affect the results.
"I do know for a fact that he is the biological father," said Sala, who is representing herself, adding that she has proof but cannot show it to the court.
She said Reeves grew up down the street from her and she has known him since she was four or five. She did not connect him to the actor until much later because she knew him by the name Marty Spencer, she said.
Lawyer Lorne Wolfson, representing Reeves, suggested Sala's ex-husband is in fact the father of the children, as is stated in documents in their divorce proceedings.
Sala has declined to bring a motion to have her ex-husband's DNA tested and has refused to produce her children's birth certificates, Wolfson said.
Reeves, 45, grew up in Toronto before leaving for Hollywood in 1986. He starred in the "Matrix" films as well as "Speed" and "Bill & Ted's Excellent Adventure."
There is no basis to her spousal or child support claims, and as such there is no reason the matter should go forward, Wolfson said. He brought a motion Thursday that the case should not go to trial.