Madonsela's attitude was that she was superior to the Constitution and superior to Parliament, Duarte told reporters in Johannesburg.
"We all need to work on that to be corrected because we actually need to strengthen the office of the public protector."
Duarte said the African National Congress was concerned by "a public protector who is very populist in her orientation and sometimes does not present the full picture to the public".
Duarte was responding to questions during a briefing to give feedback on a National Working Committee meeting held on Monday.
She questioned the leaks coming from Madonsela's office. Duarte said the leaks were worrying as they seemed to be calculated.
Among those was a letter Madonsela reportedly wrote to President Jacob Zuma last week about the spending of R246 million on security upgrades at his Nkandla, KwaZulu-Natal homestead.
In her letter she cautioned him that he was second-guessing her recommendations that he should repay part of the money spent on features unrelated to security, such as a swimming pool, cattle kraal, amphitheatre, and visitors' centre.
In his reply to her report on Nkandla, Zuma indicated Police Minister Nathi Nhleko needed to determine if he should pay back any of the R246 million.
Madonsela wrote in her letter: "I am concerned that the decision you have made regarding the police minister gives him power he does not have under law, which is to review my decision taken in pursuit of the powers of administrative scrutiny I am given... by the Constitution."
Madonsela said on Monday that she had reason to believe a senior ANC official had leaked her letter to the media.
Duarte questioned the manner in which the explanations for the leaks were given, but individuals not named.
"Each leak is glibly explained away. Who is that senior official who leaked the letter? There is nothing unfortunate about the leaks, they are timed and deliberate," Duarte said.
Duarte and ANC secretary general Gwede Mantashe questioned the timing of the leaking of the letter and the heckling of Zuma in Parliament by members of the Economic Freedom Fighters, after the EFF asked when Zuma would pay back the Nkandla money. Proceedings had to be stopped for the day and riot police were called in.
"A leak at the same time when the EFF undermines the people of SA is too much of a coincidence," said Duarte.
Mantashe echoed the sentiments and said the issues they had both raised were the same.
"Even more curious is that some MPs claim to have seen the public protector in the Parliamentary Precinct on the same day. Without accusing anybody, the tight co-ordination of this offensive is interesting," said Mantashe.