"The presidency cannot continue to function with a spokesperson of questionable credibility," said Democratic Alliance national spokesperson Mmusi Maimane.
"Mr Maharaj's presence undercuts the very legitimacy of the office he serves. It cannot continue," he said.
Maimane said he would write to Zuma on Friday to ask that Maharaj be suspended.
"The ever-increasing stack of allegations brought forward by the Mail & Guardian, in particular the allegations made by Mr Maharaj's sister-in-law, seems to suggest that Mr Maharaj did in fact receive a kickback from Thales – the French weapons manufacturer that bribed Schabir Shaik," said Maimane.
"If the allegations by Mr Maharaj's sister-in-law are in fact true, a direct link can be drawn between Mr Maharaj and Thales, via the Swiss bank account he allegedly opened to facilitate Thales' payments to him."
Kickbacks on a 1990s contract
The newspaper reported that Maharaj's sister-in-law Shirene Carim told it about a Swiss bank account, into which proceeds of kickbacks on a 1990s contract for new drivers' licences were allegedly paid.
Maharaj's lawyers told the newspaper this was not the first time the claim was being made, but it had not been published or acted on until now because of its origin and "lack of veracity".
"Responsible journalism requires of you to treat these false, and undoubtedly uncorroborated allegations in a similar light," BDK Attorneys director Rudi Krause wrote in a response to journalist Sam Sole.
Carim told the M&G her sister had told her, during a stop-over in London on her way to open the bank in account in Geneva in 1996, that Shaik was getting a tender "because he was a good comrade during the struggle".
"She was going to Geneva because she was getting this money from this guy who was getting the tender," she reportedly said.
According to the M&G, a Scorpions investigation into Maharaj obtained documents which showed that money was later transferred into the account from a company which was in a consortium with Shaik to produce the new credit-card style drivers' licences.
The case against Maharaj, who was transport minister at the time, was later withdrawn. The newspaper described Carim's move as apparently driven by "courage and bitterness, anger and principle", and reported that Shaik, who claimed not to know Carim, had said there appeared to be "some family breakdown".
In response to the DA's request, Maharaj said he was in London and so did not know if the request had been submitted yet by the DA.
He directed a request for comment on the article to Krause. However, Krause said he had not read it yet because he had been in court, and that he would not be able to say anything immediately, as he was also due to travel. – Sapa