The station reported on its website that Rowe had said she was willing to submit to any testing, including DNA, to prove she was the biological mother of Prince Michael, 12, and Paris, 11.
"I am stepping up," Rowe added. "I have to."
Rowe, who was married to Jackson for three years from 1996, also said she was willing to undergo psychological testing in any custody claim.
NBCLA said Rowe would also seek a restraining order to keep Jackson's father, Joe Jackson, away from the children.
Rowe has been largely silent since the sudden death of Jackson, 50, on June 25 from an apparent cardiac arrest.
On Monday, a Los Angeles court named the star's 79-year-old mother Katherine Jackson as the temporary guardian of Prince Michael, Paris and younger brother Prince Michael II, who was born to a secret surrogate.
A 2002 will filed in Los Angeles Superior Court on Wednesday revealed that Jackson wanted his mother to gain custody of his children in the event of his death, with soul legend Diana Ross named as a back-up guardian.
Rowe signed away her parental rights to her two children in 2001, describing Jackson as a "wonderful man... a brilliant father."
However a Los Angeles judge reversed the order in 2004 after Rowe cited concerns over publicity related to Jackson's prosecution for child molestation.
Rowe later settled the case with Jackson, reportedly securing visitation rights to the children.
Legal experts have been split on whether any move for custody by Rowe is likely to be successful.
Family law attorney Fred Silberberg said Rowe stood an excellent chance of securing custody of Prince Michael and Paris.
"Generally speaking in California, biology trumps everything," Silberberg told AFP last week.
"Courts tend to favor the biological parents so in that regard she has a very strong case," Silberberg said, drawing comparisons to O.J. Simpson, who successfully saw off a custody challenge from the grandparents of ex-wife Nicole Brown-Simpson, who he was accused of murdering in 1994.
However other experts say Rowe's chances of success could hinge on her relationship with the children. She has reportedly had only minimal contact with the children for several years.
"If she has a strong relationship with her children and... she has seen them somewhat regularly then she has a very strong chance of getting custody," said Scott Altman, a law professor at the University of Southern California.
"But if ... she hardly has visited with her children, they have no relationship at all, they don't think of her as a mother it will be very difficult for her to get custody."
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