Police have opened a criminal investigation against Sarney's businessman son on suspicion he abused his family connections to win lucrative deals with state companies.
The senate is also accused of having passed "secret acts" in which taxpayers' money was spent on controversial items, including upping public servants' salaries, without any publication.
Sarney, who took charge of the senate in February, last month said he did not know of any secret acts. But this week he nullified 663 that had come to light.
He also insists that a two-million-dollar house undeclared on his electoral record in fact belonged to his daughter, and that he had no control over the Jose Sarney Foundation which received money from the state-run oil company Petrobras.
Lula, who needs the backing of Sarney's Brazilian Democratic Movement Party to govern with his Workers' Party, has defended Sarney and deflected calls from for the senate leader's resignation.
But he stirred the pot by calling opposition senators "pizza-makers" for establishing a probe into Petrobras's finances, using a Brazilian term that refers to frequently unsuccessful corruption scandals.
That angered senators, who have prepared a motion calling for Lula to apologize.
Brazil's congress was going through "a terminal crisis of credibility," the senator behind the motion, Cristovam Buarque, told AFP.
The country's Tourism and Hospitality Workers Confederation has also expressed indignation at the slur against real Brazilian pizza-makers.
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