In an interview on Irish television channel RTE, the former Republic of Ireland captain refused to apologise for the outburst that saw McCarthy send him home from Japan.
Nobody wants to play for Ireland more than me... but the ball is not in my side of the court
And he insisted it was up to McCarthy and others to make the first move if any reconciliation was to take place before the tournament gets underway.
In response, John Delaney from the Football Association of Ireland (FAI) told RTE he didn't think Keane's latest statement was enough to resolve the dispute.
Indeed, Keane's tone in the interview was defiant rather than apologetic.
He told RTE: "I am standing firm for what I believe in. What happened to me last week was wrong.
"My conscience is clear, that's the most important thing.
"If there was any doubt in my mind, then maybe I would have held back a little bit.
"But there isn't and I won't accept it. I can't accept it.
"Nobody wants to play for Ireland more than me. It's the biggest thing to play in the World Cup.
"We'll have to wait and see, maybe there is a way, but the ball is not in my side of the court."
An apology from Roy would be absolutely vital before anything moved forward
FAI's John Delaney
Keane's lawyer, Michael Kennedy, had hoped the interview would pave the way for his return to the squad.
But the statement is unlikely to persuade McCarthy to even contemplate allowing him back into the squad.
The manager - and some of his players - have already made it clear they will not bow to any pressure from officials or the Irish public to take Keane back.
In the interview, Keane also reiterated his earlier attack on fellow players Steve Staunton, Niall Quinn and Alan Kelly for not backing him.
And he claimed he was left to arrange his own transport home after the bust-up with McCarthy.
"The senior players knew the score, but they let it all happen.
"There was only going to be one winner, and that was Mick.
"But I felt I deserved better. I wouldn't wish what happened on anybody, it will live with me for a long time."
The journalist who interviewed Keane, Tommie Gorman, concluded the Manchester United star was "deeply emotional about what has happened.
"He is still willing, still yearning to play for Ireland in this year's World Cup," Gorman added.