Janet, Randy and Rebbie Jackson said in an attorney's statement issued on their behalf that their aim was only to replace the executors of their brother's multimillion-dollar estate, who they accuse of mismanagement.
The statement followed two weeks of Jackson clan infighting, including a trip by family matriarch Katherine Jackson, 82, to Arizona in which she has said she was cut off from the outside world and was reported missing.
Jackson, who died in June 2009, appointed his mother guardian of his three children, and made the children beneficiaries of his estate. His father and eight siblings were not included.
"It is important to stress that Janet, Randy and Rebbie have questioned the validity of the will with no financial motive whatsoever - they stand to gain nothing financially by a finding that the will is invalid," Friday's statement said.
"What will be gained ... is that the executors will be replaced and the estate and the guardianship will be managed in a manner that is in the best interests of the children," it added.
Michael Jackson's estate is managed by a music executive and a lawyer. According to recent court documents, the estate has earned $475 million in gross profits since the singer died of an overdose of the surgical anesthetic propofol.
The executors have said that any doubts about the validity of Jackson's will were debunked two years ago in a legal challenge that went all the way to the California state supreme court.
But Friday's statement said that "Janet, Randy and Rebbie will continue to press forward in their search for the truth in order to carry out the wishes of their brother Michael."
The bitter dispute has led to Janet, Randy and Rebbie being barred from visiting their mother and Jackson's children at their home near Los Angeles following an angry altercation there last week.
Brothers Jermaine and Tito Jackson have backed down from the public campaign to throw out the will, and appealed instead for family unity.
(Reporting by Jill Serjeant; Editing by Eric Walsh)
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