On March 21, Latham appeared on Sky to accuse Ms Keneally, the former NSW premier, of being a "prot??g??" of disgraced former NSW Labor minister Eddie Obeid.

Five days later, on his Sky program The Outsiders, Latham lashed out at Ms Harmer after she wrote on social media that she was "deeply unimpressed" by some of Sky's offerings.

Latham instructed the veteran broadcaster to "tune out" and "get a life".

He then claimed she was a "commercial failure" who got a job at the "sheltered workshop" ABC because she is a woman with a disability.

Ms Harmer sent a legal letter to Sky News over the remarks and wrote on Twitter: "To be clear, a simple apology will do."

Latham, the former federal Labor leader, has since been sacked over a separate incident where he speculated that a Sydney schoolboy was "gay" after the teenager appeared in a video about feminism.

The apology was delivered on Thursday night, about 13 minutes into the 6pm news bulletin.

"A statement now from Sky News management," newsreader Ashleigh Gillon began.

"Sky News acknowledges that it broadcast certain statements by Mark Latham about Wendy Harmer. Sky News acknowledges that these statements falsely imputed that Ms Harmer's media career over the past four decades has been a failure, and that she has only been able to secure her current employment as a broadcaster with the ABC because she is a female with a disability.

"Sky News rejects these comments in their entirety and apologises unreservedly to Ms Harmer."

The apology also acknowledged the network had broadcast "certain statements" by Latham about Kristina Keneally.

"Sky News acknowledges that these statements falsely imputed that Ms Keneally acted corruptly in her former role as premier of NSW. Sky News rejects these comments in their entirety and apologises unreservedly to Ms Keneally."

Following the apology, Ms Harmer wrote on Twitter: "Thank you Sky News for my unreserved apology"