Kroenke, whose father Stan owns KSE, made the statement during a hostile fans forum with Gunners supporters on Thursday afternoon.
During it Kroenke, who is a director at Arsenal, was grilled about the club’s involvement in the Super League.
It was confirmed at the forum that Kroenke and the KSE would cover the cost of Arsenal leaving the Super League.
CEO Vinai Venkatesham, who was also at the meeting, explained the cost of that was below the reported £8million figure.
Kroenke also reiterated his family’s commitment to Arsenal as, when asked when KSE planned to sell the club or what their exit strategy was, he replied: “I am not willing to answer that question because we have no intention of selling.”
Kroenke added: “I believe we are fit to carry on in our position as custodians of Arsenal. “We were put in a very difficult position by forces outside of the club.
“We have the same plans for summer that we had several weeks ago and I’m still excited about those.
“So I might be met with mistrust, I might be met with scepticism, but over time I hope to establish some sort of relationship with our supporter groups and show them that we are capable of taking our club forward.”
Kroenke admitted during the meeting KSE made a mistake in joining the Super League and they had damaged their relationship with fans.
“I am well aware we have never really had trust and what teeny bit of hope there was among a small fan group that KSE would take it forward, I know that has been shredded as well,” he said.
“That is why I am here to start to build that bridge. If ever there ever was a plank on the bridge or no planks on the bridge of trust, I am here to start trying to build that bridge.
“We were rushed into a decision… We would consult with a lot more people, including supporter groups. To be frank, we know how everyone feels about the proposal as constructed.”
Kroenke added: “I think from an English fan’s perspective, and this is what was so educating for me, they want to see more big matches.
“But as one Chelsea supporter wrote on a sign that I saw online the other day, you still want your cold nights in Stoke. I think to me that sent a strong message of the English Premier League, football in the UK as a whole and the fan sentiment across England. We got it wrong, and that is why we are here today.”