The petition to sack Kay Burley has gathered support after Ofcom confirmed that it has received in excess of 1,100 complaints about the broadcaster's interview with Nick Varney.
Varney, who is chief of Merlin Entertainment, which owns Alton Towers, was grilled by Burley after a crash at the theme park that left 16 people injured.
The petition on Change.org states that the interview was "awful" and that Burley was "rude" on the Sky News programme.
At the time of writing, the petition was just 50 people shy of the 35,000 target.
The petition posits the argument that Burley should be sacked.
It reads: "This interviewing is an embarrassment to Sky News, she was rude and patronising not giving him chance to explain and when he did get chance to explain she continued to dismiss his comments and further trying to damage the company thinking that she was clever.
"She also tried to get him to give highly confidential private information on the casualties. He didn't try to shift responsibility he knew enormously what this event did, shut the park and is fully investigating the incident working with authorities.
"What happened at Alton Towers was awful and it shouldn't have happened but what happened at your Sky studio was awful too and shouldn't of happened, now you need to put this right, act professional like the CEO did, issue an apology and sack Kay Burley."
The crash at Alton Towers on 2 June meant customer Leah Washington, 17, subsequently had her leg amputated above the knee.
Burley was criticised for what some believed to be her aggressive interview style when talking to Varney.
"People were seriously injured, and there are suggestions that someone's lost a limb as a result of what happened at Alton Towers," she said. "Has somebody lost a limb on that ride?"
When Varney said that Merlin Entertainment was "deeply sorry" for the accident, Burley responded saying that she was "sure [the family] are not interested in your sympathy at this stage."
Ofcom confirmed that it had received 1,162 complaints about the interview. The media watchdog will assess the complaints before deciding whether to launch an investigation.
In March, 131 complaints were sent to Ofcom regarding a perceived "bias" against Ed Miliband following the leaders' debates.Reuse content