She however stopped short of apologising to the paper for claims that its journalists were acting on the instructions of unnamed "handlers" when they ran a series of articles about her.
Pule called a press conference on April 22 and claimed that journalists Mzilikazi wa Afrika, Stephan Hofstatter and Rob Rose were running a smear campaign against her.
She claimed the journalists' "handlers" wanted to influence the outcome of a lucrative tender to supply set-top box sets to the department. The boxes allow televisions to receive digital signals.
According to the paper, less than 24 hours after Pule’s press conference, her lawyer Ronnie Bokwa contacted the newspsper and said he had been instructed to broker an "armistice".
"We have wronged the Sunday Times," Bokwa reportedly said.
But Pule has not apologised for her claims, in spite of demands from the paper that she provide proof of her claims or publicly retract them. The paper sent Pule a lawyer's letter and gave her until last Friday to respond.
On the day of the press conference, Sunday Times editor Phylicia Oppelt demanded an apology from Pule. The following day, the newspaper said Bokwa called wa Afrika and said Pule's department had asked him to broker a "peace process".
Meetings with Pule were arranged, but the newspaper said that Pule failed to arrive, instead sending her deputy-director general Themba Phiri to apologise on her behalf.
"I don't know why the minister did not come through," Bokwa reportedly told the paper.
Meanwhile, a parliamentary probe into Pule's role in arranging the ICT Indaba in 2012 began behind closed doors on Friday. The nine-member Parliamentary committee will investigate claims that Pule's partner Phosane Mngqibisa unfairly benefited from the indaba.
Pule has refused to answer further questions related to the inquiry. At the April 22 press conference she appealed to journalists to allow the Parliamentary process to take its course.
Pule is also facing a probe by the public protector as well as a corruption probe by the police.