The presidency told the Mail & Guardian on Friday that President Jacob Zuma "did not use the word 'constitution'" earlier this week, with spokesperson Mac Maharaj saying "he did not say he wants to change the Constitution."
On Wednesday, several media outlets reported that Zuma told hundreds of ANC supporters in KaNyamazane, near Nelspruit, to vote ANC to ensure the party gets a two-thirds majority in order to make changes to South Africa's most prominent piece of legislation.
However, he did not specify how he wants to change it.
"We want a huge majority this time because we want to change certain things that couldn't be changed with a small majority so that we move forward because there are certain hurdles. People talk about a constitution they have never seen. We saw that constitution," he said.
'Forever and ever'
He later said the ANC would govern "forever and forever".
The presidency also released a statement on Friday saying the Constitution is "not static" and is a "transformative document".
Maharaj said there was "nothing untoward" about "wishes to amend any part of the Constitution".
"There is nothing inappropriate about amending the Constitution provided it's done within the law and the Constitutional Court is there to oversee the procedure," he told the M&G.
According to the statement, the Constitution has been amended 18 times, as recent as November 2012.
Zuma was in Nelspruit ahead of the ANC's January 8 statement and to launch its election manifesto at the Mbombela Stadium on Saturday.