Democratic Alliance parliamentary leader Lindiwe Mazibuko said Zuma had to come clean on whether he saw a letter outlining security upgrades for Nkandla.
"If he did see the letter, then he must further clarify why he did not take any steps to address the unnecessarily excessive expenses set out in the letter... and whether he accordingly made any enquiries as to their cost," Mazibuko said in a statement.
The department of public works had sent a letter to Zuma in November 2010.
On Sunday, Nxesi said the government spent R206 million on security upgrades and consultants. Included in this amount was R135 million for the "operational needs" of various government departments, R71 million for consultants and security features such as bullet proof windows, security fencing, evacuation mechanisms, and firefighting equipment, he told reporters in Pretoria.
Also included in the total was R26 million to make changes to the project (variation orders).
Nxesi said the task team investigating the spending found irregularities in the appointment of the 15 service providers and consultants who worked on the project.
State Security Minister Siyabonga Cwele said on Sunday that neither Zuma nor his family had any input on the security upgrade.
"They were not involved with the design and installation of security measures."
Nxesi said Zuma was informed of the upgrades, but did not know any of the details.
Mazibuko said the letter contradicted Nxesi's "concerted campaign" to prove the report on Nkandla vindicated Zuma.
The Inkatha Freedom Party said it was becoming another "presidential embarrassment".
"The Minister of Public Works Thulas Nxesi has stated that there were irregularities in the appointment of service providers and the procurement of goods and services at President Zuma's home in Nkandla," IFP MP Petros Sithole said in a statement.
"A full investigation must be launched into this matter as a matter of urgency."
The Freedom Front Plus and the Christian Democratic Party questioned the amount spent on Nkandla.
FF Plus spokesman on public works Pieter Groenewald said: "It is possible to have effective security measures put in place for far less than the amount mentioned."
Groenewald said the full report should be made public. Nxesi said it would not because the residence was a national key point.
Corruption Watch (CW) said it had written a letter to Nxesi asking for a copy of his task team's report.
It also wanted the minister to publish the names of the companies or individuals who were awarded contracts.
"The information on the awarding of contracts does not fall within information relating to security measures and we see no reason for keeping this away from the public," executive director David Lewis said in a statement.
"Considering the public money spent on the upgrade, it is appropriate for the minister to reveal the details of the tendering process as well as explain how the amounts mentioned in Sunday’s press briefing were arrived at and budgeted for."
The Congress of SA Trade Unions in Gauteng said the report revealed nothing new.
"In fact, some of these issues are ones we have been raising for some time -- the fact that government has no capacity to do anything. Everything is outsourced," provincial secretary Dumisani Dakile said.
He said it was "not surprising" that corrupt officials benefited unfairly by outsourcing work on the home.
"People in government must choose whether they want to serve the people, or they want to be in business. We know for a fact that there are people who are charging the state R200 for a loaf of bread," said Dakile. - Sapa