"We distance ourselves from this leak because it is a serious matter and we will approach the relevant security agencies to investigate," Motshekga said in a statement.
"We apologies [sic] to Mr Nxasana for the mishap."
The Sunday Times reported that Nxasana sent an SMS to Motshekga last Monday after a child called her "brainless" in one of FNB's "You Can Help" videos.
"Good Morning Minister. I have instructed FNB to remove the video clips from their website this morning. I will investigate how and why the clips ended [up] on their website. Sincere apologies for this. Sizwe," the SMS read.
The FNB campaign features a number of videos of children in school uniform reading their hopes for the country. The ANC said the campaign "bordered on treason", while opposition parties and activist groups called the ruling party's criticism of the campaign intolerant.
FNB changes tack
Meanwhile, FNB took out full-page advertisements in four national newspapers on Sunday in the aftermath of the ANC's criticism of its "You Can Help" campaign.
The text of the adverts, published in the Sunday Times, City Press, Sunday Independent, and Rapport, appear in five stanzas, each beginning with the line: "We help because we believe".
It concludes with the words, in bold type: "We help because we believe where there's help, there's a way."
FNB met with ANC leaders, including secretary general Gwede Mantashe, on Thursday. The bank apologised to the party on Friday.
But the apology was met with disapproval.
'Disappointment'
University of Free State vice-chancellor Jonathan Jansen posted on Facebook on Saturday: "I am deeply disappointed by FNB for running to apologise/explain to a political party for airing the voices of children. Does FNB realise how much blood was spilt for the right to say what you think? I fear for my country."
Democratic Alliance (DA) leader Helen Zille tweeted on Saturday: "Saying that #FNB caved in order to protect the kids in the advert is a more devastating statement on the ANC govt than anything the ad said."
Ambassador to Argentina and former DA leader Tony Leon tweeted: "The ANC must be laughing all the way to the bank."
City Press editor Ferial Haffajee tweeted: "I wonder when we who get bullied say so far and no more? Not a good feeling at all."
During the meeting on Friday, the ANC reportedly argued the campaign sought to project the party and government in a negative light. The ANC said the clips had a negative impact on business confidence and could undermine investment in the country.
First National Bank CEO Michael Jordaan said he would not resign.
"I am not resigning as CEO [of] the most innovative bank in the world," he tweeted on Friday morning. – Sapa