"Due to the need to continue discussion with regional and national NAACP leaders, tomorrow's meeting is postponed and will be rescheduled for a later date," the chapter said in a statement Sunday.
Dolezal's estranged parents have accused her of falsely portraying herself as black for years, claiming she is white.
The revelation sparked a nationwide controversy on race and identity, especially because she is president of the local NAACP chapter and is chairwoman of a police oversight committee.
"We are her birth parents," her father, Lawrence Dolezal, said Friday. "We do not understand why she feels it's necessary to misrepresent her ethnicity."
After the meeting was postponed, the head of the chapter's executive committee criticized the decision.
"I don't see any language in the by-laws that empowers you, or any one member, to arbitrarily cancel/postpone tomorrow's meeting," Lawrence Burnley said in a letter to Dolezal.
Rachel Dolezal declined an interview when contacted by CNN last week, but said she stands by her record of service. She said she would address the accusations Monday night at the now postponed meeting.
Dolezal has said she received threatening hate mail in the past, but the Spokane Police Department told CNN's Poppy Harlow that it dropped its investigation on the letters because of lack of leads. The investigation was dropped before the controversy about her race became public.
Adopted brother speaks out
More of her relatives have joined the chorus of criticism.
Her adopted brother, Ezra Dolezal, said she took him aside three years ago and asked him "not to blow her cover" about her alternate identity.
"She said she was starting a new life ... and this one person over there was actually going to be her black father," Ezra Dolezal said.
Dolezal has identified herself as at least partly African-American, but her Montana birth certificate states she was born to two parents who say they are Caucasian. The parents shared that document and old photos with CNN.
She began identifying herself more with the African-American community in 2007, according to her parents.
Chapter supports her
The regional NAACP leader has said her race is not a factor.
What Dolezal has done is more important than what race she is to the NAACP, regional President Gerald Hankerson said. He called the NAACP a civil rights organization first that includes "leaders from all different ethnicities," adding that it "doesn't do a genealogy search on what a person's ethnicity is when they" take a top position.
"We represent all civil rights issues, regardless of a person's ethnicity. And the quality of the work that she has done to elevate the issues of civil rights in that region is what we applaud," he said.
A peaceful protest against Dolezal is planned outside the NAACP office in Spokane tonight, CNN affiliate KXLY reported.
CNN's Stephanie Elam, Paul Vercammen, Greg Botelho, Tony Marco and Ralph Ellis contributed to this report.