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8 year oldA spokesman for the interim President, Michel Temer, said she would have been placed in the stand below him and not at his side.
Her predecessor, Luiz Inacio Lula da Silva, has also refused the invitation despite being instrumental in Rio's winning bid to host the games.
Both have said they are being politically persecuted by Mr Temer's party and allies.
Ms Rousseff faces possible removal from office if she loses an impeachment trial shortly after the games and Lula is facing corruption allegations, which he denies.
What has gone wrong with Brazil?
Another former President, Fernando Henrique Cardoso, has also said he will not attend the ceremony.
Ms Rousseff has said that she believes she should be at the ceremony alongside Lula.
She told Radio France International on Monday that her government and Lula's had done most of the work to win the Olympics for Rio de Janeiro and find the financing to build the infrastructure for the global sports event.
Diplomats have said the presence of both Michel Temer and Dilma Rousseff at the ceremony would have been awkward for foreign dignitaries.
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