Jones stormed off the set of Sunday night’s paper review after host Mark Longhurst and guest Julia Hartley Brewer suggested the killing of 50 people in Pulse, an LGBT club was similar to the attack on the Bataclan in Paris in November.
This was condemned by veteran LGBT rights campaigner Peter Tatchell, who told The Mirror: “The line of questioning put to Owen Jones would never have been put to a black or Jewish person if one of their venues had been attacked in this way.”
Jones had said: “At the end of the day this was a homophobic crime, as well as terrorism and it has to be called out.”
Longhurst said: "Whether I’m gay or not has no reflection on the fact that this person killed 50 people."
After a few tense moments of further discussion of the papers, Jones removed his microphone and walked out.
A statement from Longhurst on Monday afternoon expressed "regret" over the broadcast.
"As the presenter responsible for chairing the conversation, I regret that the segment ended as it did," he said.
"I absolutely accept the atrocity in Florida was, of course, an attack on LGBT people, but I was also trying to reflect what was on the newspaper front pages. It was never my intention to offend Owen Jones and I very much look forward to working with him again in future."
It left Jones unimpressed. He tweeted it was "the definition of non-apology".
Almost 60 people have so far lodged complaints with the regulator Ofcom over the programme.
Tatchell, an Australian-born veteran of campaigner for LGBT rights said: "I think the interviewer should sit down with people from the LGBT community to discuss our concerns. There was widespread anger in the LGBT community at that interview."
Writing in The Guardian on Monday, Jones said his storming off was "an instinctive reaction to an unpleasant and untenable situation".
"If a terrorist with a track record of expressing hatred of and disgust at Jewish people had walked into a synagogue and murdered 50 Jewish people, we would rightly describe it as both terrorism and an anti-Semitic attack," he wrote.
"If a Jewish guest on television had tried to describe it as such, it would be disgraceful if they were not only contradicted, but shouted down as they did so. But this is what happened on Sky News with a gay man talking about the mass murder of LGBT people."
He added: "It is possible for an atrocity to be more than one thing at the same time. You are not compelled to select one option or the other. Life – with both its horrors and its joys – is incredibly complicated, and we have a rich language able to capture its complexities."
On her TalkRadio show, Hartley-Brewer said she had received a barrage of abuse after what happened but said she would not "check my white straight privilege at the door".
“I will not check my white straight privilege at the door. I will speak as I find and I will always speak as I find because I live, thank God, in a free, Western, liberal democracy," she told her listeners.
She denied she was a "homophobe" as tweets she received suggested.
“I have spent most of the night getting abuse from people who claim that I’m homophobic for stating repeatedly that this was a homophobic attack and how awful it was but apparently I didn’t use exactly the right form of words," she said.
"Owen is a very good friend... He took exception to something the host said.
"We repeatedly stated it that [the shooting] was a homophobic attack. We were trying to have a debate about why this man had been motivated to make a homophobic attack.
Tatchell spoke to Hartley-Brewer later on her show.
She said to him: "Fifty people were killed because they were gay but for me, actually human beings were killed."
He said she was "right" but added: "Had this been an attack on black people by white supremacists, it would've been absolutely right for us to focus on the racism, the violent racism that we needed to call out.
"That's simply what we are trying to say about this particular attack. Of course, they were human beings but they were also very specifically LGBT people and their allies in that club."