Hussain made his outburst after England were forced to forfeit their Group A match against Zimbabwe for refusing to play in Harare over security and ethical concerns.
England and Wales Cricket Board chief Tim Lamb said: "I spoke twice to Hussain before his press conference Saturday to assure him he had the total and unequivocal support of the board.
"I don't know (if he'll stand down), I think perhaps in the emotion of the moment he said what he did, we'll have to wait and see," he told the BBC by telephone from South Africa.
"There is no intention of replacing him."
Hussain said on Saturday he and his team felt let down by the International Cricket Council and the ECB. The players feel the ICC failed to take their security concerns seriously while the ECB wanted the Harare match to go ahead so as to avoid possible compensation claims.
"I don't blame him for being rather frustrated and emotionally drained after the events of recent weeks," Lamb said, adding he was confident the ECB would not liable for financial damages for pulling out of the Zimbabwe game.
"We do believe there is no factual or legal basis on which we could be found liable to pay any damages," he said. "We think we've got a valid 'force majeure' event."
Lamb said, if financial penalties were levelled at the ECB, a figure of three million dollars was likely in respect of the television rights.
Zimbabwe and South Africa, both due in England this year, have suggested they could cancel their tours in retaliation after England's refusal to play in Harare but Lamb countered: "It should be remembered that all countries make the lion's share of their income from international cricket.
"Nothing is to be gained from cancelling tours and I very much hope that, once the dust has settled over this whole unfortunate episode, normal business will be resumed."
