All seven Komen affiliates in California, in a joint letter to their congressional delegation, said they were "strongly opposed" to the policy change and were working to overturn it.
"Our commitment to our mission is unwavering," the letter said. "This is a misstep in that journey and ... we will do whatever it takes to do what is right for the health of women and men in California."
In New York City, a member of the Komen affiliate's medical advisory board said she would resign if the decision wasn't changed soon.
"Komen is a wonderful organization and does tremendous things for women, but this is straying from their mission," said Dr. Kathy Plesser, a radiologist. "It's sad."
The board of the Arkansas affiliate issued a statement noting that the decision was made at Komen headquarters "without input from affiliates," and called for the new policy to be changed.
"We hope Komen national will reverse its position on granting to organizations under investigation because we feel decisions of this nature should be made only after the investigation is complete," the statement said.
At the Orange County affiliate in Costa Mesa, Calif., executive director Lisa Wolter said there have been lots of exchanges with headquarters.
"We're very troubled by the reaction, and we want to make sure there are clarifications," she said.
The American Association of University Women, in protest over Komen's decision, said it was scrapping plans to offer a Komen Race for the Cure as one of the activities at its upcoming National Conference for College Women Student Leaders.
"AAUW is disappointed that some are playing politics with women's health and jeopardizing care for the most vulnerable among us," said Lisa Maatz, the association's director of public policy.
According to Planned Parenthood, its health centers performed more than 4 million breast exams over the past five years, including nearly 170,000 as a result of Komen grants.
Though comments posted on Komen's Facebook page seemed to be mostly critical of the grant decision, Brinker said at her news conference that donations to the charity had increased since Tuesday.
She also said there were other organizations receiving Komen grants, in addition to Planned Parenthood, that might be adversely affected by the new criteria about investigations, but she did not identify them.
Susan G. Komen for the Cure: http://ww5.komen.org/
Planned Parenthood: http://www.plannedparenthood.org/
David Crary can be followed on Twitter at http://twitter.com/CraryAP
Copyright 2012 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.