Calm has returned to the streets of Pretoria following a chaotic march against immigrants on Friday..
"We don't want to remove the public protector, we want the public protector to do her work correctly and behave correctly," Mantashe told reporters in Johannesburg.
"We have no interest in removing her. She must finish her term but she must not abuse that term."
Mantashe said there was a sense that Madonsela was abusing her office and was always trying to get the attention of the media by saying things that were not in any report or being investigated anywhere.
"That is what we are talking about. That is why we are not attacking the public protector or her office but we are attacking the behaviour that is wrong," he said.
Mantashe then turned his attention to the leaking to the media of Madonsela's reports. He said the leaks could not be attributed to divisions within the ANC.
The statement follows Madonsela's claim that a letter she had written to President Jacob Zuma was leaked by a senior ANC official to the media.
Madonsela reportedly wrote to Zuma last week about the spending of R246 million on security upgrades at his Nkandla, KwaZulu-Natal homestead.
In her letter, she cautioned Zuma 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 leaked her letter to the media.
Mantashe countered: "The office of the public protector leaks every report she writes and blames that on the divisions within the ANC."
Mantashe said it had become the norm that all public protector reports would be leaked to the media before she had even released them.
"I know that every report she has been involved in... I'm going to read about it in the newspaper before it is released.
"That can never be because of divisions in the ANC. We deal with our own divisions but the public protector's office must be watertight. You can't leak information and blame the ANC divisions," he said.
Mantashe and his deputy Jesse Duarte continued hammering the issue of leaks and 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 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 called on Madonsela not to get involved in politics and to stop behaving like a political institution.
He said the public protector should get out of the political space and leave political parties to sort themselves out.
Madonsela then took to twitter to defend herself against the barrage of attacks by the pair. She stood her ground and questioned how accountability was weakening democracy.
"Can someone please say how exactly is the deepening of accountability a weakening of parliamentary democracy... Let's face th truth. What's embarrassing the country is attempts to subvert the rule of law & not administrative scrutiny [sic]," she said.
Madonsela said if everyone respected the Constitution and the law, there would be no crisis in the country.
She said politicians should stop interfering with her work.
"Administrative scrutiny is a reality if our constitutional democracy. It's not a political exercise & Politicians should stop interfering [sic]," she tweeted.
Madonsela said the country was in trouble when politicians meddled in the investigation processes, leaked documents then cried foul.
The EFF on Tuesday denied any link to the leaking of the letter and their heckling of Zuma.
Spokesman Mbuyiseni Ndlozi said the ANC was trying to detract attention from the Nkandla issue.
"The ANC has lost the public relations war and now they have to concoct a story to defer the issue that is on the table, which is Nkandla," he said.
Ndlozi accused Zuma of being the one who leaked the document to the media.
"If there is anyone with a history of leaking information it is Jacob Zuma to distract the public's attention as we saw with the Mzilikazi [waAfrika] story," he said.
In his book, waAfrika claims that Zuma leaked information about Bulelani Ngcuka being a former apartheid spy.
Ndlozi called on the ANC to stop attacking Madonsela's office.
"We condemn in the strongest way the continuing intimidation and war that has been declared on the public protector," he said.