Dilma Rousseff accused her opponents of causing a political crisis which she said had damaged the economy.
She also defended her predecessor, Luiz Inacio Lula da Silva, over money-laundering allegations.
Dilma Rousseff said a prosecutors’ request for his detention had no legal basis.
The ongoing crisis has deepened the worst recession in decades in Brazil – Latin America’s biggest economy.
Dilma Rousseff said she had been democratically elected and had no intention of going.
The inquiry has implicated several business leaders and politicians close to the government including Luiz Inacio Lula da Silva.
Regional prosecutors in Sao Paulo want Luiz Inacio Lula da Silva, 70, placed in “preventive custody” after charging him with failing to declare ownership of a luxury sea-front penthouse in the seaside resort of Guaruja.
They say this is necessary because he may try to obstruct the investigation. The request still has to be accepted or rejected by a judge.
The former president denies any wrongdoing and says the claims are politically motivated. He says he never owned the apartment.
His lawyer, Cristiano Zanin Martins, said Brazil’s ex-leader had invested in the project and had visited the unfinished apartment but later asked for his money back rather than receiving the property.
President Dilma Rousseff refused to comment on a possible cabinet job for Luiz Inacio Lula da Silva but said she would be proud to have him in her government.
Last week, the former president was briefly detained and questioned in a separate, federal investigation into whether extensive refurbishment on the penthouse had constituted favors in exchange for political benefit.
The renovations were carried out by one of Brazil’s biggest construction companies, OAS.
Officially the apartment belongs to OAS, which is itself accused of paying bribes to politicians and senior officials at state oil company Petrobras to secure lucrative contracts.
In addition, federal prosecutors are looking into allegations that Luiz Inacio Lula da Silva sold his influence in President Dilma Rousseff’s administration in exchange for donations to his Instituto Lula non-profit foundation.
Last week’s questioning of Luiz Inacio Lula da Silva led to criticism not only from his supporters but also from judges and politicians, who said it was unnecessary.
His supporters say the attacks on him are aimed at tarnishing his reputation, amid rumors that he may run for office again in 2018.
Luiz Inacio Lula da Silva was Brazil’s left-leaning president from 2003 to 2011 and was succeeded in office by his political protégé, Dilma Rousseff, who has record-low approval rates amid a serious economic crisis.
A former factory worker and union leader, Luiz Inacio Lula da Silva remains a very popular figure in Brazil despite the accusations against senior members of the Workers’ Party.
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